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Qri)oms0n*s  lixQi  Ccssons. 

MENTAL 

ARITHMETIC, 

OB 

FIRST    LESSONS    IN    NUMBERS 

FOR    CHILDREN. 
By  JAMES  B.  THOMSON,  LL.D.,^ 

AUTOOU  Ol»  PaAOTlOAI.  ARITUMBTIO,  BDITOB  OP  DAY'h  SOHOOl  AMHBOA 
I.BOBNDRli'8  QBOMSTRV,  BTO. 

ONI   HUNDRED    AND   FIFTIETD   EDITION,   REVISED   AND  BNLABOBD. 


NEW  YORK: 
CLARK  &  MAYNARD,  6  BARCLAY  ST. 

CHICAGO  :    a  C.  GRIGGS  &   CO. 

*  *  *  * 


1 


BiiUjkxI  oooordlDg  to  Act  of  OongrcBe,  In  Uie  ytor  iy3€, 

By  JAMES  B.  THOMSON, 

in  the  Clerk'u  OflJoo  of  the  Northern  Dlstrlot  of  Now  York. 


PREFACE 


At  what  precise  age  a  child  should  begin  to  gc  to  schoal, 

or  commence  the  different  studies,  it  is  not  our  province  to 

I  decide.     Whatever  may  be  the  diversity  of  opinion  on 

I  this  point,  all  practical  teachers  seem  to  agree,  that  Men- 

\  id  A^thmetic  is  among  the  first  exercises  which  should 

j  be  presented  to  the  youthful  mind.     The  correctness  of 

I  this  sentiment  is  corroborated  by  the  ease  with  which 

I  children  understand  simple  combinations  of  numbers,  their 

!  fondness  for  the!>e  exercises,  and  the  obvious  advantages 

I  which  may  be  derived  from  them.     But  in  order  to  be- 

I  come  interesting  or  profitable,  it  is  manifest,  this  branch, 

j  as  well  as  others,  must  be  taught  in  such  a  manner  that 

the  pupil  shall  understand  it.     The  examples,  therefore, 

j  must,  at  first,  be  simple,  containing  small  numbers,  and 

have  reference  to  sensible  objects  with  which  the  learner 

is  accjuainted  ;  the  transition  from  easy  to  more  difficult 

(questions  must  be  gradual;   and  the  reason  for  every 

step  in  the  solution  distinctly  seen. 

It  is  believed  that  much  dislike  for  the  study  of  Arith- 
metic, and  much  unnecessary  discourage7nent,  have  been 
occasioned  by  the  abruptness  of  the  transitions  from  easy 
to  difficult  questions.  It  is  too  often  forgotten  that  the 
powers  of  the  child's  mind,  Lke  those  of  his  body,  are 
feeble ;  that  while  familiar  mental  exercises  which  he  can 
comprehend,  afford  him  the  highest  delight,  he  turns  from 
intricate  questions,  which  he  does  not  and  cannot  under- 
itand,  with  indifference  and  disgust. 

It  is  the  design  of  this  little  work  to  furnish  a  ser^^  of 
mental  exercises  in  numbers,  adapted  to  the  wants  and 
cnparities^of  children.  It  commences  with  practical  ex- 
amples, which  relate  to  familiar  objects  and  require  the 


PREFACE. 


simplest  combinations.  The  pupil  is  then  introduced  to 
others  involving  the  same  principle  but  somewhat  harder, 
special  care  being  taken  to  make  the  transition  very  grad- 
ual, so  that  instead  of  being  disheartened  at  the  rugged- 
ness  of  the  way,  he  shall  be  stimulated  to  take  the  next 
step  by  the  hope  of  victory. 

From  the  fact  that  children  comprehend  and  remember 
words  more  easily  than  figures,  and  reason  upon  them 
with  so  much  greater  facility,  the  numbers  and  Tables 
in  the  first  part  of  the  book  are  expressed  in  words. 

After  the  pupil  has  become  practically  acquainted  with 
the  principles  of  a  rule,  and  is  able  to  solve  questions  un- 
der it  with  facility,  the  operation  is  then  defined,  and  the 
more  prominent  terms  are  briefly  explained.  This,  it  is 
believed,  teachers  will  be  glad  to  see.  There  is  no  rea- 
son why  a  child  should  not  be  informed,  that  a  certain 
operation  upon  numbers  is  called  Addition ;  another  Sub- 
traction ;  &c.,  as  well  as  to  be  told  that  a  certain  opera- 
tion of  his  vocal  organs  in  connection  with  those  of  his 
mind,  is  called  reading  ;  another  singing ;  &c. 

With  this  brief  explanation  of  the  object  and  plan  of 
the  work,  the  author  commends  it  to  the  friends  of  edu- 
cation, by  whom  his  former  efforts  to  subserve  this  noble 
cause, have  been  so  favorably  received. 

Although  designed  particularly  as  an  introduction  to 
the  *'  Practical  Arithmetic,"  it  may  be  used  as  a  prepar- 
atory work  to  any  of  the  larger  systems  of  Arithmetic 
now  aefore  the  public. 


MENTAL    ARITHMETIC. 


SECTION    I 


INTRODUCTION, 


The  first  step  in  acquiring  a  knowledge  of  numbers  is 
to  learn  to  count.  Most  children  are  able  to  repeat  the 
na7}ies  of  numbers,  one,  two,  three,  (Sec,  before  they  begin 
to  go  to  school ;  but  there  are  fewer  who  fully  comprehend 
the  meaning  of  these  terms;  who  perceive,  for  example, 
that  eleven  expresses  more  things  than  seven,  or  fewer 
than  thirteen.  While  such  is  the  case,  no  substantial 
progress  can  be  made  in  Arithmetic. 

Great  pains  should  therefore  be  taken  to  show  young 
pupils,  in  the  outset,  how  many  things  thf»  name  of  each 
number  denotes,  and  to  establish  in  their  minds  a  correct 
idea  of  more  and  less.  Counters,  made  of  round  pieces 
of  wood  or  leather,  also  beans,  kernels  of  com,  &c.,  may 
be  used  for  this  purpose  ;  but  the  most  convenient  appa- 
ratus is  the  Numerical  Frame.*  The  bails  upon  the 
wires  are  more  easily  arranged  and  are  seen  at  once  by 
every  member  of  the  class,  while  the  liability  of  falling 
upon  the  floor  and  getting  lost,  is  entirely  avoided. 

LESSON    I. 

Having  slipped  all  the  balls  to  the  left  side,  the 
teacher  holds  up  the  Numerical  Frame  before  the 
class  and  requests  their  particular  attention. 

•  Every  instniclor  who  is  called  upon  to  tearh  the  nidimfntfl  of 
Arithmetic,  should  be  furniBhed  wiih  this  useful  instrument,     it 


INTRODUCTION. 


With  his  pointer  he  now  moves  the  first  ball  on 
the  bottom  wire  to  the  right  side  and  says,  this  is 
oiie,  the  class  repeating  it  with  him.  Moving  across 
another  on  the  same  wire,  he  says,  this  makes  two, 
the  class  repeating  it  with  him  as  before ;  moving 
an  )ther,  this  makes  three  ;  another  still,  this  makes 
'  four  ;  and  yet  another,  this  makes  Jive  ;  and  so  on 
up  to  ten. 

Tliis  process  should  be  repeated  and  varied  ac- 
cording to  circumstances,  u.itil  the  class  can  count 
ten  in  concert  and  individually  with  readiness.  If 
this  cannot  be  accomplished  in  one  exercise,  another 
should  be  devoted  to  it. 

Note.—U  the  (hil<lr»»n  are  young,  or  have  never  learned  the 
names  of  any  of  the  numbers,  when  they  get  to  three  or  Jive  h  will 
l)e  ^xp«?nient  to  stop  and  review  as  far  as  they  have  been.  Care 
Hhould  be  taken  not  to  present  too  many  new  ideas  to  the  young 
mind  at  once,  lest  it  become  bewildered  ;  nor  should  the  exercise 
be  continued  so  long  as  to  weary  it,  and  thus  create  a  lasting  dis- 
relish for  the  study. 

LESSON    II. 

Slippine  a»:  the  balls  to  the  left  side  of  the  frame 
as  before,  move  the  first  on  the  lower  wire  to  ihe 
right  side,  and  ask  the  class  to  count  it. 

Now  move  out  two  on  the  second  wire,  taking 
one  at  a  time,  and  let  the  class  count  as  you  niuve 
them,  one,  tioo.  Then  pass  across  three  on  the  third 
wire,  taking  one  at  a  time,  while  the  class  coimt 
one,  two,  three. 


costs  but  a  trifie,  and,  with  proper  care,  will  last  an  age.     Us 
raore  important  uses  will  be  pointed  out  in  their  proper  place. 

The  lessons  in  this  Section  are  designed  for  pupils  who  have 
not  learned  to  count,  or  may  not  comprehend  how  many  things 
are  dr«noted  by  the  names  of  numbers.  I'hose  who  thoroughly 
undeti-tand  tliese  points,  cen  begin  with  Addition. 


INTRODUCTION.  7 


Proceed  in  this  manner  to  the  iejith  or  Icist,  in- 
creasing one  ball  on  each  successive  wire. 

Again,  beginning  at  the  bottom,  let  the  class  count 
he  balls  moved  out  on  each  Avire,  and  observe  that 
two  is  one  more  than  one;  that  three  is  one  more 
than  two  ;  that  four  is  one  more  than  three,  &c. 

Next,  let  the  class   retrace  this  process ;  that  isj  | 
beginning  at  the  top,  let  them  count  the  balls  moved 
out  on  each  wire  till  they  arrive  at  the  bottom  one. 

Let  them  also  begin  at  ten  and  count  backwards 
to  one,  several  times  in  quick  succession.  Thus, 
teji,  nine,  eight,  seven,  six,  &c. 

Finally,  move  out  any  number  of  balls  under  ten 
promiscuously,  and  call  upon  some  one  to  count 
them ;  then  move  out  a  different  number,  and  let 
another  count  them ;  and  thus  continue  to  vary  the 
exercise,  till  every  one  in  the  class  can  count  ten 
understandingly. 

LESSON    III. 

Note. — As  soon  as  the  class  clearly  comprehend  how  many  thinffs 
are  expressed  by  the  name  of  each  of  the  numbers  up  to  ten,  they 
are  then  prepared  to  learn  to  count  from  ten  to  twenty,  &,c. 

Flaving  counted  out  ten  balls  on  the  lower  wire, 
move  across  one  on  the  second  wire  saying,  this 
makes  eleven,  the  class  repeating  it  with  you.  Pass- 
ing across  another,  this  makes  twelve  ;  another,  this 
makes  thirteen  ;  another  still,  this  makes  fourteen  ; 
and  so  on  up  to  twenty. 

Repeat  this  process,  at  the  same  time  explaining 
to  the  class  that  the  term  thirteen,  is  composed  of 
the  words  three  and  ten,  and  means  the  same  as  ihvf'e 
counted  on  to  ten,  or  three  and  ten  put  together. 
Also,    that   the   term  fourteen  is  con.posed  of  the 


INTRODUCTION. 


words  four  and  ten,  and  means  the  same  as  four  and 
ten  put  together;  that  fifteen  means  five  and  ten; 
sixteen^  six  and  ten ;  seventeen,  seven  and  ten;  eiyh- 
teen,  eight  and  ten;  nineteen,  nine  and  ten;  and 
twenty  means  two  tens. 

Next,  having  counted  off  twenty  balls ;  that  is, 
ten  apiece  on  each  of  the  two  lower  wiies,  pass 
across  one  on  the  next  wire,  saying  this  makes  twen- 
ty-one, the  class  repeating  it  with  you  as  before. 
Passing  across  another,  this  makes  tioenty-two  ;  an- 
other, this  makes  tioenty-three ;  another  still,  this 
makes  twenty-four  ;  and  so  on  to  thirty. 

Here  again  tlie  teacher  should  be  careful  to  ex- 
plain that  the  term  twenty-one,  is  composed  of  the 
words  iiventy  and  one,  and  means  the  same  as  one 
counted  on  to  twenty,  or  twenty  and  one  put  together. 
Also,  that  the  term  twenty-two,  is  composed  of  the 
words  twenty  and  two,  and  means  the  same  as  twenty 
and  two  put  together;  that  tzoenty- three  mea.ns  twen- 
ty and  three  ;  «fec. 

In  a  similar  manner  children  may  be  easily  taught 
to  count  from  thirty  to  forty,  fifty,  sixty,  &c.,  to  a 
hundred,  and  to  comprehend  Iiow  7nany  tilings  are 
expressed  by  the  name  of  each  number. 

Nott  to  tht  Teacher. — It  is  advisable  to  exercise  the  pupil 
in  writing  the  Jigures  upon  his  slate,  or  the  black-board,  in 
the  early  part  of  his  course.  This  will  afford  him  pleasing 
occupation,  and  at  the  same  time,  will  be  of  great  assistance 
in  enabling  him  to  understand  and  apply  them  when  he 
shall  have  occasion  for  their  use 


SECTIOJN    II. 
ADDITION. 

LESSON  I. 

1.  How  many  little  hoys  are  there  in  this  class? 

2.  How  many  little  girh  are  there  ? 

3.  How  many  little  girls  and  boys  are  there, 
counted  together  ? 

4.  Will  each  of  you  show  n  e  your  right  hand  ? 
Now  if  you  put  your  left  hand  by  the  side  of  it,  how 
many  hands  will  each  one  show  me  ?     Why  ? 

Ans.  Because  one  and  one  more  make  tv:o. 

5.  If  you  show  me  two  fingers  on  your  left  hand 
and  one  on  your  right,  how  many  fingers  will  you 
show  me  ?     Why  ? 

Ans.  Because  two  and  mie  more  make  three. 

6.  If  you  open  three  fingers  on  your  left  hand  and 
one  on  your  right,  how  many  fingers  will  you  have 
open  ?     Why  ? 

7.  How  many  fingers  have  you  on  your  right 
hand  ?  How  many  thumbs  ?  How  many  fingers 
and  thumbs  counted  together,  are  there  on  your  right 
hand? 

8.  If  I  move  out  five  balls  on  the  lower  wire  of 
Tfiy  Numerical  Frame  and  one  on  the  next,  how 
many  will  they  all  make  ?     Why  ? 

Note. — When  a  general  question  ia  asked  whicl  is  not  desi^Hd 
to  be  answered  in  concert,  it  is  an  excellent  way  to  have  afi  who  j 
think  they  know,  raise  a  hand ;  the  i  call  upon  some  one  promifl-  j 
cuously  to  answer  it.     This  methcxJ  prevents  much  confusion  and  | 
secures  the  attention,  wliile  it  effectually  avoids  the  temp'ation  , 
to  learn  the  answers  to  certain  questions  which  will  fall  to  »>ach, 
if  the  teacher  always  begins  at  the  same  end  of  the  cla^^  and 
proceeds  through  it  iii  regular  rotation. 


10 


ADDITION, 


9.  I^  I  move  out  six  on  the  lower  wire  and  one 
on  the  next,  how  many  will  they  make  ?    Why  ? 

10.  If  I  move  out  seven  on  the  lower  and  one  on 
the  next,  how  many  will  they  make  ?    Why  ? 

11.  If  I  move  out  eight  on  the  lower  and  one  on 
the  next,  how  many  will  they  make  ? 

12.  If  I  move  out  wne  on  the  lower  and  one  on 
the  next,  how  many  wi  1  they  make  ? 

Note. — A«  loon  m  a  child  learns  a  principle  in  Arithmetic,  it  i« 
iniportajit  for  him  to  see  ita  application,  ana  begin  to  practice  it. 
For  this  reason,  it  js  recommended  to  let  the  class  iludy  the  next 
eight  lessons  in  connection  with  the  corresponding  paru  of  the  Ta- 
ble be.ow.  Thus,  as  soon  as  they  learn  to  add  twos,  let  them  take 
lesson  second  yvhich  contains  exercises  in  adding  two ;  as  soon  as 
they  learn  to  add  threes,  let  them  take  lesson  third,  &c.  In  this 
way  the  Table  is  kept  together,  which  is  essential  for  reference 
ana  review,  ar.d  at  the  same  time  we  secure  all  the  advantages 
of  studying  it  jx  connection  with  examples  which  put  it  into  prac- 
tice, as  fast  as  it  is  leamexi. 

ADDITION    TABLE. 


One 

•nd 

oae     wr. 

twa 

One 

•nd  six      V  seven. 

One 

u 

two     " 

threek 

One 

"    seven  «  eight. 

One 

u 

three  " 

four. 

One 

"    eight    "  nine. 

One 

U 

four    " 

five. 

One 

"    nine    "   ten. 

One 

u 

five     " 

six. 

One 

«    ten       "   eleven. 

Two 

and 

OJtB      •« 

three. 

Two 

u»d  six      Ml  eight. 

Two 

u 

two     " 

four. 

Two 

"    seven  "   nine. 

Two 

(1 

three  " 

five. 

Two 

"    eight    "  ten. 

Two 

H 

four    " 

six. 

Two 

•'    nine    "   eleven. 

XW) 

n 

five     '* 

seven. 

Two 

"    ten       "   twelve. 

Ihree 

•Ad 

on«J    «• 

four. 

Three 

Hid  six      u*  nine. 

Three 

u 

two     " 

five. 

Three 

"    seven  "  ten. 

Three 

u 

three  " 

six. 

Thr«e 

"    eight    "  eleven 

Three 

II 

four    " 

seven. 

Three 

"    nine    "  tweha 

Three 

II 

five  .  " 

eight. 

Three 

"    ten      "  thirteen. 

1 

1 

ADDITION. 

11 

Four 

and  one 

art  five. 

Four    and  six 

are  ten. 

1  Four 

"    two 

»  «x. 

Four      "    seven 

"  eleven.        ( 

1  Four 

'     three 

"  seven. 

Four      "  .eight 

"  twelve. 

!  Four 

'     four 

"  eight. 

Four      "    nine 

«♦  thirf.'en.     | 

i  Four 

«    five 

"  nme. 

Four      "    ten 

**  fourteen. 

;  Five 

and  one 

are  six. 

Five     and   six 

are  eleven. 

Five 

"    two 

"  seven. 

Five      "    seven 

"  twelve. 

Five 

"    three 

"  eight. 

Five      "    eight 

"  thrrieen. 

Five 

«    four 

"  nine. 

Five      "    nine 

"  fourteen 

Five 

"    five 

"  ten. 

Five      "    ten 

"  fifteen. 

Six 

ana  one 

ar«  seven. 

Six          and    six 

are  tWclve. 

Six 

»    two 

"  eight. 

Six       '"    seven 

"  thirteen. 

1  Six 

"    three 

"  nine. 

Six        "    eight 

"  fourU^en. 

Six 

"    four 

"  ten. 

Six        '<    nine 

«  fifteen. 

Six 

"    five 

*'  eleven. 

Six        "    ten 

"  sixteen. 

Seven 

aud  one 

are  eight. 

Seven  and  six 

are  thirteen. 

Seven 

'»    two 

"  nine. 

Seven    "    seven 

"  fourteen. 

Seven 

"    three 

"  ten. 

Seven    "    eight 

"  fifteen. 

Seven 

"    four 

"  eleven. 

Seven    "    nine 

"  sixteen. 

Seven 

"    five 

"  twelve. 

Seven    "    ten 

"  seventeen. 

Eight 

and  one 

are  nine. 

Eight     and    six 

are  fourteen.     I 

Eight 

"     twn 

"  ten. 

Eight     "    seven 

"  fifteen.        | 

Eight 

"    thific 

"  eleven. 

Eight      "    eight 

"  sixteen. 

Eight 

«    fom 

'*  twelve. 

Eight      "    nine 

"  seventeen. 

Eight 

"    five 

**  mirteen. 

Eight     "    ten 

*•  eighteen,     j 

!  Nine 

and    one 

are  ten. 

Nine     anu   six 

are  fifteen.      - 
"  sixteen. 

Nine 

"    two 

"  eleven. 

Nine       "    seven 

Nine 

"    three 

"  twelve. 

Nine       "    eight 

"  seventeen. 

Nine 

«    four 

"  thirteen. 

Nine      "    nine 

'*  eighteen,     j 

j  Nine 

1 
1 

«    five 

"  fourteen. 

Nine      "    ten 

"  nineteen. 

12  ADD7TI0N. 


LESSON   II. 

1.  If  a  pear  costs  two  cents,  and  an  apple  costs  one 
cent,  ho^  many  cents  will  they  both  cost  ?     Why  ? 

2.  Charles  had  ttao  books,  and  his  father  gave  him 
two  more:  how  many  books  did  he  then  have? — 
Why? 

3.  Robert  brought  in  three  sticks  of  wood,  and 
George  two  sticks :  how  many  sticks  did  both  boys 
bring  in  ?     Why  ? 

4.  Let  each  one  in  the  class  open  all  his.  fingera 
on  his  left  hand,  and  two  on  his  right :  how  many 
fingers  has  each  one  open  ?  How  many  are  four 
and  two  ? 

5.  Sarah  had  Jive  dresses,  and  on  her  birthday 
her  aunt  gave  her  two  more  :  how  many  dresses  had 
she  then  ?     Why  ? 

6.  In  this  class  there  are  two  girls,  and  six  boys  : 
how  many  scholars  does  the  class  contain  ? 

7.  John  has  seven  brothers,  and  two  sisters :  how 
many  brothers  and  sisters  has  he  together  ? 

d.  A  little  boy  gave  a  blind  man  eight  cents,  and 
his  sister  gave  him  two  cents  more  :  how  many  cents 
did  they  both  give  him  ? 

9.  William  has  two  marbles  in  his  hand,  and  nint 
in  his  pocket :  how  many  marbles  has  he  in  all  ? 

10.  Mary  recited  two  perfect  lessons  last  week  and 

^1  Nole. — llje  process  of  addins  and  the  structure  of  the  Table 
raay  be  easily  illustrated  by  the  Numerical  Frame.  Thus,  to  show 
that  five  and  four  make  nine,  mi-ve  out  five  balls  on  one  wire  and 
four  on  another,  and  let  the  pupil  count  them  together.  But  as 
I  soon  as  the  pupil  understands  the  principle  of  the  oiHiration,  he 
should  tlien  learn  to  i»crforra  it  without  the  assistance  of  visible 
objects.  Nothing  is  more  deleterious  to  mental  growth  and  dis- 
cipline, than  the  habit  of  solving  questions  by  counters,  by  the 
fingers,  marks  upon  a  slate,  &c.  (S^n. 


ADDITION.  13 


tfifi  this  wee.i :  how  many  perfect  lessons  has  sK-e  re- 
cited in  two  weeks  ? 

LESSON   III. 

1     If  you  pay  three  cents  for  a  pint  of  nuts,  and  I 
one  cent  for  an  apple,  how  many  cents  do  you  pay 
for  boili  ?     Why  ? 

2.  Henry  has  tkree  young  doves,  and  two  old  j 
ones :  how  many  doves  has  he  ?     Why  ? 

8.  A  begjxar  met  some  generous  little  boys,  one 
of  whom  gave  him  four  cents,  and  another  gave  him 
three  cents:  how  many  cents  did  they  both  give 
him  ?     Why  ? 

4.  Susan  bought  three  yards  of  blue  ribbon,  and 
three  yards  of  white  :  how  many  yards  of  ribbon  did 

I  she  buy  in  all  ?     Why  ? 

5.  Harriet  gave  her  teacher  Jive  pinks,  and  three 
roses :  how  many  flowers  did  she  give  her  teacher  ? 

6.  Matthew  sold  a  quart  of  chestnuts  for  6ix  cents, 
and  a  pint  of  beechnuts  for  three  cents:  how  much 
did  his  nuts  come  to  ?  i 

7.  flenry  picked  three  ripe  peaches  from  one  lree>  I 
and  s€i'>en  from  another :  how  many  peaches  did  lie  ' 
pick  from  both  trees  ?  I 

8.  Frank  has  nme  walnuts  in  his  pocKet,  and  he  j 
lost  three  coming  to  school :  how  many  had  he  when 
he  started  from  home  ? 

9.  How  many  are  eight  and  three  ?  I 

10.  Jane  read  ten  pages  of  hislory  in  the  morning, ' 
and  three  in  the  afternoon  :  how  many  pages  did  slm  i 
read  during  the  day  ?  I 

Ncte. — It  is  ad\l8able  lo  have  the  class  review  iIjc  prerrdinjr  i 
part  of  the  Table,  and  thus  continue  to  do  at  every  re-itati(jn,  ! 
till  they  get  through  it.  { 


14  ADDITION. 


LESSON  IV. 

1.  Joseph  received  four  peaches  from  his  couiiin. 
and  one  from  his  sister :  how  many  peaches  had  he  ? 

2.  A  boy  paid  four  cents  for  an  orange  and  two 
cents  for  a  pear :  how  much  did  he  pay  for  both  ? 

3.  Emily  bought  a  yard  of  silk  for  five  shillings, 
and  a  pair  of  gloves  for  four  shillings :  how  many 
shillings  did  she  pay  for  both  ? 

4.  Dick's  father  gave  him  six  marbles,  and  he 
gained  four  more :  how  many  had  he  then  ? 

5.  Henry  gave  four  cents  for  a  lemon,  and  four 
cents  for  an  orange :  how  many  cents  ^lid  he  give 
for  both  ? 

6.  A  farmei  g^yefour  dollars  for  a  hog,  and  eight 
dollars  for  a  cow :  how  much  did  he  pay  for  both  ? 

7.  How  many  are  four  and  three  ? 

8.  A  market  boy  soldybwr  shillings  worth  of  milk, 
and  vegetables  to  the  amount  of  ^even  shillings:  how 
much  money  did  he  have  to  carry  home  ? 

9.  James  g&yefour  shillings  for  a  knife,  and  nine 
shillings  for  a  pair  of  skates:  what  did  he  pay  for 
both? 

10.  Henrietta  bought  a  slate  for  ten  cents,  and  a 
sponge  for  four  cents :  how  much  did  she  pay  for 
both? 

LESSON   V. 

1.  A  man  bought  a  plough  for  fve  dollars;  and  a 
•hovel  for  two  dollars :  how  many  dollars  did  he  pay  \ 
for  both  ?  j 

2.  A  farmer  raised  three  bushels  of  plums    n  one  | 
tree,  and  j?re  bushels  on  another :  how  many  bushels 
did  he  raise  on  both  trees  ? 


ADDITION.  15 


I  3.  A  man  sold  a  bushel  of  plums  fear  five  dollars, 
and  a  bushel  of  peaches  (or  four  dollais:  how  much 
did  both  come  lo  ? 

4.  There  are  six  sweet  apples,  said  five  sour  ones  , 
I  in  the  fruit  dish:  how  many  apples  does  the  dish 

contain  ?  j 

5.  A  man  paid^t'e  shillings  for  a  turkey,  &nd  five 
shillings  for  a  peck  of  peas:  how  much  did  he  pay 
for  both  ? 

6.  A  man  caught  eight  red  squirrels,  erndfive  grey 
ones :  how  many  did  he  catch  in  all  ? 

7.  A  cabinet-maker  asks  five  dollars  for  a  rock- 
ing  chair,  and  seven  dollars  for  a  table :  what  is  the 
price  of  both  ? 

8.  If  I  pay  five  shillings  postage  on  letters,  and 
nine  shillings  on  pamphlets,  what  is  the  amount  of 
my  postage  ? 

9.  Harriet  bought  a  comb  for  ten  cents,  and  a  pa- 
per of  needles  ioT  five  cents :  how  much  did  she  pay 
for  both  ? 

LESSON  VI. 

1.  Charlotte  picked  six  white  roses,  and  two  red 
ones  :  how  many  roses  did  she  pick  ? 

2.  Harriet  gave  three  cents  for  a  sponge,  and  six 
cents  for  a  slate :  how  many  cents  did  she  pay  for 
both? 

3.  IIow  many  are  six  and  six  ? 

4.  How  many  are  six  ^nd  five  ?  Y 

5.  How  many  are  six  and ybwr? 

6.  If  you  read  six  pages  in  the  morning,  and  seven 
in  the  evening,  how  many  pages  will  vou  read  in  a 
day  1 


1 8  ADDITION. 


7.  John  hoed  ei^ht  rows  of  cca*n  in  one  day,  and 
s,x  in  another  day:  aow  many  rows  did  he  hoe  in 
bolh  days  ? 

8.  His  employer  gave  him  nine  pence  for  liis  first 
day's  work,  and  six  pence  for  the  second  day 's  work  : 
how  many  pence  did  John  receive  ? 

9.  A  lady  bought  a  muff  for  J^n  dollars,  and  a  hat 
for  six  dollars :  what  was  the  amount  of  her  bill  ? 

LESSON  VII. 

1.  Sarah  had  seven  pins  on  her  cushion,  and  she 
afterwards  found  two  more :  how  many  pins  had  she 
then? 

2.  How  many  are  seven  and  three  ? 

3.  If  seven  flower  pots  stand  in  one  window,  and 
foiir  in  another,  how  many  are  there  in  both  win- 
dows ? 

4.  How  many  are  seven  and  six? 

5.  How  many  are  seven  snid Jive? 

6.  How  many  are  seveii  and  seven? 

7.  Oliver  paid  seven  cents  for  a  writing-book,  and 
eig/it  cents  for  a  slate:  how  much  did  he  pay  for 
both? 

8.  How  many  are  seven  and  ten  ? 

9.  How  many  are  seven  and  nine  ?  ft 

LESS  jN  VIII. 

1.  If  a  barrel  of  flour  cost  eight  doLars,  and  a  keg 
cf  lard  'wo  dollars,    how  much  will  Wh  cost? 

*2.  A  merchant  tailor  asks  eight  liars  for  a  pair 
of  pants,  and  three  dollars  for  a  vest:  what  is  the 
price  of  both  ? 


ADDITION.  17 


3.  If  you  pay  eight  cents  a  mile  for  the  use  of  a 
horse,  and  Jive  cents  for  a  buggy,  how  much  will  you  j 
pay  a  mile  for  both  ?  i 

4.  How  many  are  6(i0'/i/ and  yb?/r?  ! 
f>.  Julius  gave  one  of  his  companions  six  ap*  '*3,  i 

and  had  eight  left :  how  many  had  he  at  first  ?  | 

6.  Henry  had  eight  marbles,  and  his  brother  gave 
him  eight  more :  how  many  did  he  then  have  ? 

7.  A  shopkeeper  sold  eight  yards  of  satin  to  one 
lady,  and  seven  to  another:  how  many  yards  did  he 
sell  to  both  ? 

8.  Catharine's  book  has  eight  pictures  in  it,  and 
iMary's  has  7une  :  how  many  pictures  do  both  books 
contain  ? 

9.  If  you  pay  eight  cents  for  a  pound  of  sugar, 
and  ten  cents  for  a  pound  of  figs,  what  must  you 
pay  for  both  ? 


LESSON    IX. 

1.  There  are  nine  shade  trees  standing  in  front  of 
the  school  house,  and  two  have  been  cut  down :  how 
many  trees  were  set  out  ? 

2.  Alexander's  kite  line  is  now  nine  yards  long, 
i  by  accident  he  broke  off  three  yards:  how  long  was 

his  line  at  first  ? 

3.  flow  many  are  ni?ie  and  Jive? 

4.  IIow  many  are  iwie  smd four? 

5.  If  a  ton  of  coal  costs  nine  dollars,  and  a  co.-d 
of  wood  costs  s^ix  dollars,  how  much  will  they  both 

jCOSt? 

I      6.  A   hunter  gave  nine  dollars   for  a  gun,  and 
I  seven  dol  ars  for  a  dog :  how  much  did  he  pay  for 

\  both  ? 

I 


18 


ADDITION, 


7.  If  you  have  nine  chestnuts  in  cne  pile  and  nine 
in  another,  how  many  will  they  make  i(  you  put 
thtm  all  into  one  pile  ? 

8.  In  Margaret's  flower  garden  there  are  nine 
lady's  slippers,  *nd  eight  bachelor's  buttons:  how 
many  flowers  has  she  ? 

9.  Sophia  wrote  nine  lines  at  the  last  exercise, 
and  Henrietta  wrote  ten :  how  many  lines  did  both 
write  ? 


LESSON   X* 

1 .  Ilow  many  are  one  and  ten  ?  Three  and  ten  ? 
Six  and  ten  1  Four  and  ten  ?  Seven  and  ten.  Five 
and  ten  ?    Eight  and  ten  ?    Nine  and  ten  ? 

2.  How  many  are  eleven  and  ten  ?  Twenty-one 
and  ten  ?  Forty-one  anjd  ten  ?  Thirty-one  and  ten  ? 
Fifty-one  and  ten  ?  Seventy-one  and  ten  ?  Sixty -one 
and  ten  ?    Eighty-one  and  ten  ?   Ninety-one  and  ten  ? 

3.  Two  and  ten  ?  Twelve  and  ten  ?  Twenty-two 
and  ten  ?  Forty-two  and  ten  ?  Thirty -two  and  ten  ? 
Fifty-two  and  ten  ?  Seventy -two  and  ten  ?  Sixty-two 
and  ten  ?   Eighty-two  and  ten  ?  Ninety-two  and  ten  ? 

4.  Three  and  ten  ?  Thirteen  and  ten  ?  Twenty- 
three  and  ten  ?    Forty-three  and  ten  1    Thirty-three 

!  and  ten  ?  Sixty-three  and  ten  ?  Eighty-three  and 
ten  ?  Fifty-three  and  ten  ?  Seventy-three  and  ten  ? 
Ninety-three  and  ten  ? 

5.  Four  and  ten?  Fourteen  and  ten?  Twenty-four 
and  ten  ?  Fifty-four  and  ten  ?  Thirty-four  and  ten  ? 
Sixty-four  and  ten  ?  Forty-four  ar  d  ten  ?  Eighty-four 

*  TJiis  and  the  following  Lesson  should  he  studied,  1 11  the  ques- 
tions can  be  answered  with  great  faril'ty. 


ADDITION.  19 


1  and  ten  ?     Seventy-four  and  ten  ?     Ninety-four  and 
Iten  ? 

I      6.  Five  and  len  ?    Twenty-five  and  ten  ?  Fifteen 
,  and  ten  ?  Seventy-five  and  ten  ?    Sixty-five  and  ten  ? 
!  Fifty-five  and  ten  ?  Forty-five  and  ten  ?  Ninety-five 
and  ten  ?  Eighty-five  and  ten  1 

7.  Six  and  ten  ?  Eight  and  ten  ?  Twenty-six  and 
ten  ?  Twenty-seven  and  ten  ?  Seventeen  and  ten  ? 
Sixty-eight  and  ten  ?  Thirty-six  and  ten  ?  Fifty- 
seven  and  ten  ?  Seventy-six  and  ten  ?  Eighty-eight 
and  ten  ? 

8.  Seven  and  ten  ?  Twenty-nine  and  ten  ?  Forty- 
seven  and  ten  ?  Thirty-six  and  len  ?  Ninety-seven 
and  ten  ?  Seventy-six  and  ten  ?  Sixty-nine  and  ten  ? 
Seventy-seven  and  ten  ?     Eighty-seven  and  ten  ? 

9.  Nine  and  ten  ?  Eighteen  and  ten  ?  Twenty- 
nine  and  ten  ?  Thirty-eight  and  ten  ?  Sixty-nine 
and  ten  ?  Fifty  eight  and  ten  ?  Seventy-nine  and 
ten  ?  Forty-nine  and  ten  ?  Eighty-nine  and  ten  ? 
Ninety-nine  and  ten  ? 

LESSON    XI 

1 .  How  many  are  twelve  and.  five  ?  Twenty-two 
and  five  ?  Forty-two  and  five  ?  Thirty -two  and  five  ? 
Fifty-two-and  five?  Seventy-two  and  five  ?  Sixty- 
two  and  five  ?  Eighty-two  and  five  ?  Ninety-two 
and  five  ? 

2.  How  many  are  thirteen  and  six  ?  Twenty-three 
and  six  ?  Thirty-three  and  six?  Forty-three  and 
six  ?  Seventy-three  and  six  ?  Fifty-three  and  six  ? 
Eighty-three  and  six  f  Sixty-three  and  six  ?  Ninety- 
three  and  six  ? 

8.  How  many  are  fourteen  and  seven  ?  TAventy- 
four  and  seven  ?  Forty-four  and  seven  ?  Thirty-four 


*20  ADDITION. 


and  seven  ?  Fifty- four  and  seven?  Seventy-four  and 
seven  ?  Sixty-four  and  seven  ?  Eighty-four  and 
^even  ?  Ninety-foui  and  seven  ? 

4.  How  many  are  fifteen  and  eight  ?  Twenty. five 
And  eight  ?  Sixty-f^ve  and  eight  ?  Forty-five  and 
eight  ?  Seventy-five  and  eight  ?  Thirty-five  and 
eight?  Ninety-five  and  eight?  Eighty-five  and 
eight? 

5.  How  many  are  sixteen  and  nine  ?  Thirty-six 
and  nine  ?     Twenty-six  and  nine  ?    Forty-six  and 

I  iiine  ?     Eighty-six  and  nine  ?     Sixty-six  and  nine  ? 
Ninety-six  and  nine  ? 

6.  How  many  are  seventeen  and  three  ?  Twenty- 
jseven  and  four  ?  Thirty-seven  and  five  ?  Forty- 
seven  and  six  ?  Fifly-seven  and  seven  ?  Sivty-seven 
and  eight  ?     Eighty-seven  and  nine  ? 

7.  How  many  are  eighteen  and  two  ?  Twenty- 
eight  and  three  ?  Thirty-eight  and  four  ?  Forty- 
eight  and  five  ?  Fifty-eight  and  eight  ?  Sixty-eight 
and  seven  ?  Seventy-eight  and  six  ? 

8.  How  many  are  nineteen  and  nine  ?  Twenty- 
nine  and  eight  ?  Thirty-nine  and  seven  ?  Forty-nine 
and  six  ?  Fifty-nine  and  five  ?  Sixty-nine  and  four  ? 
3eventy-nine  and  three  ? 

9.  How  many  are  five,  thirteen,  two,  and  one  ? 

10.  How  many  are  six,  fourteen,  five,  and  ten  f 

11.  How  many  are  two,  three,  sixteen,  and  four? 

12.  How  many  are  three,  four,  seven,  and  two* 

13.  How  many  are  fifteen,  and  ten,  and  seven,  I 
And  five,  and  three  ?  | 

14.  How  many  are  thirteen,  and  seven,  and  five, 
and  ten,  and  four  ?  i 

15.  How  many  are  sixteen,  and  four   and  three,  j 
and  seven  ?  I 


ADDITION.  21 


LEiSSON    XII 

i 

1.  A  grocei  sent  me  a  pound  of  t^a  worth  seven  I 
shillings,  a  gallon  of  molasses  worth  three  shillings, ! 
and  a  pound  of  honey  worth  one  shilliiig  :  how  many  | 
shillings  did  they  all  amount  to  ?  | 

2.  IIow  many  are  ten,  and  fourteen,  and  two  ?        ' 

3.  IIow  many  are  seven,  and  fifteen,  and  three  ?    1 

4.  How  many  are  sixteen,  and  three,  and  two, ! 
and  one  ? 

5.  Charles  bought  a  pound  of  raisins  for  ten  cents, 
a  quart  of  strawberries  for  six  cents,  and  a  stick  of 
candy  for  one  cent :   what  was  the  cost  of  all  ? 

6.  One  of  Samuel's  hens  has  sixteen  chickens, 
another  has  seven,  and  the  other  three :  how  many 
chickens  has  he  in  all  ? 

7.  In  my  walk  this  morning  I  saw  nineteen  wild 
geese  in  one  flock,  eight  in  another,  and  five  in  an- 
other :   how  many  wild  geese  did  I  see  ? 

8.  Sixteen,  and  five,  and  three  are  how  many  ? 

9.  Seventeen,  and  six,  and  fuur  are  huw  many  ? 

10.  Ten,  and  seventeen,  and  three  are  how  many  ? 

11.  Horatio  paid  ten  cents  for  a  peukaife,  ten  cents 
for  a  slate,  five  cents  for  an  inkstand,  and  one  cent 
for  a  pencil :  how  many  cents  did  he  pay  for  all  ? 

12.  A  man  paid  fifteen  dollars*  for  a  cow,  eight  dol- 1 
lars  for  a  load  of  hay,  three  dollars  for  a  calf,  and  i 
two  dollars  for  a  sheep :  how  many  dollars  did  he ' 
pay  for  all  ?  j 

13.  Henry  bought  a  Spelling- Bo :)k  fcr  ten  ccntS;  , 
I  an  Arithmetic  for  twenty  cents,  and  a  slate  for  nine 

!  cents  :  how  nmch  did  he  pay  for  all  ? 

j      14.  Twenty,  and  ten,  and  seven,  and  three,  and  ! 

;  five  are  how  many  ? 


J 


22  ADDITION. 


LESSON    XIII. 

1.  Q.  What  is  the  operation  called,  by  which  the 
precedinsj  examples  have  been  solved  ? 

Ans.  It  is  called  Addition, 

2.  Q.  What  is  addition  ? 

Ans.  Addition  is  tlie  process  of  uniting  two  or  more 
numbers  in  one  sum. 

3.  Q.  What  is  the  answer^  or  number  obtained,  by 
addition,  called  ? 

Ans.  The  sum  or  ammint. 

4.  Q.  When  we  say  fve  and  four  are  nine  ;  which 
of  these  number  is  the  sum  or  amount  ? 

When  we  say  eleven  and  eight  are  nineteen^  which  is 
the  sum  or  amount  ? 

5.  Q.   What  is  the  sum  of  six,  and  four,  and  two  ? 
Solution. — Six    and    four  are  ten,    and   two  are 

twelvie.     Ans.  Twelve. 

6.  What  is  the  sum  of  five,  and  three,  and  one  ? 

7.  What  is  the  sum  of  eight,  and  four,  and  three  ? 

8.  What  is  the  sum  of  ten,  and  fifteen,  and  two  1 

9.  What  is  the  f^m  of  twenty,  and  six,  and  four  ?  | 

10.  What  is  the  ^um  of  thirty-one,  and  tf.n,  and  | 
six,  and  one,  and  four  ?  I 

11.  What  is  the  sum  of  twenty-seven,  and  three,  j 
and  one,  and  six,  and  five  ?  I 

'12.  What  is  the  sum  of  forty-three,  and  four,  and  j 
ten,  and  six,  and  seven  ? 

13.  What  is  the  sum  of  fifty-four,  and  five,  and  j 
nine,  and  three,  and  six  ?  j 

14.  What  is  the  sum  of  seventy-two,  and  three,  j 
ind  five,  and  seven,  and  eight  ? 

IT).   What  is  the  sum  of  sixty-eight,  and  ten,  and 
two,  and  five,  and  three,  and  nine  ? 


ADDITION.  23 


EXAMPLES    FOR    PRACTICE. 

Note.  —The  examples  for  practice  may  be  divided  into  two  or 
more  lessons  according  to  tlie  capacity  of  the  learner.  | 

I 

I .  It  cost  a  traveler  ten  shillings  a  day  for  his 
i  board,  seven  shillings  for  his  horse,  and  three  shil- 
i  lings  for  incidental  expenses  :  how  much  were  his 
j  daily  expenses  ? 

j      2.  If  one  little  girl  should  give  rne  "Jeven  roses, 

j  another  five  tulips,  and  another  four  pinks,  how  many 

I  flowers  should  1  have  1 

j      3.   Mow  many  are  three,  and  seventeen,  and  four  ? 

!      4.  How  many  are  sixteen,  and  four,  and  five  ? 

I      5.  How  many  are  eighteen,  and  four,  and  two  ? 

I      6.  A  man  bought  a  pound  of  sugar  for  ten  cents, 

j  a  pound  of  raisins  for  eight  cents,  and  a  pound  of 

i  butter  for  six  cents :  what  was  the  cost  of  all  ? 

I      7.  Henry   bought  a  quart  of  cherries  for  eight 

I  cents,  an  orange  for  tliree  cents,  and  an  ounce  of 

!  pep})ermints  for  six  cents :  how  much   did  he  pay 

i  for  all  ? 

I      8.  Five,  and   three,  and   seventeen,  and  one,  are 

I  how  many  ? 

'      9.  Sixteen,   and  two,   and  seven,  and  three,  are 

how  many  ? 

10.  Three,  and  nineteen,  and  seven,  and  two,  are 

how  many  ? 

II .  f  larry  bought  a  pound  of  raisins  for  ten  cents, 
a  pound  of  figs  for  fifteen  cents,  and  an  orange  for 
five  cents  :  what  did  they  all  amount  to  ? 

12.  Louisa  gave  twenty  cents  for  her  slate,  ten 
cents  for  her  writing-book,  six  cents  for  8   bunch  of 


24  ADDITION. 

. ! 


quills,  and  three  cents  for  some   pencils :  what  did 
she  pay  for  all  ? 

13.  How  many  are  four,  and  five,  and  one  ?  Six, 
and  seven,  and  three  ?  Three,  and  eiji^ht,  and  four  ? 
Six,  and  ten,  and  five  ?     Ten,  and  eight,  and  three  ? 

14.  How  many  are  eight,  and  two,  and  four  ?  Six, 
and  one,  and  two  ?  Seven,'  and  four,  and  ten  ? 
Nine,  and  ten,  and  five  ? 

<?15.  A  farmer  sold  a  cow  for  eleven  dollars,  a  calf 
for  four  dollars,  and  a  sheep  for  three  dollars  :  how 
much  did  he  receive  for  all  ? 

16.  A  gentleman  had  several  apple-trees  in  h's 
garden  ;  frofn  one  he  gathered  seven  hushels,  from 
another  ter.  and  from  another  five  bushels:  how 
many  bushels  did  he  gather  from  all  ? 

17.  Dick  bought  a  knife  for  twenty-five  cents,  and 
sold  it  for  five  cents  more  than  he  gave  for  it :  how 
much  did  he  sell  it  for  ? 

15.  A  man  bought  a  sleigh  for  thirty  dollars,  and 
paid  seven  dollars  to  have  it  painted,  and  ten  dollars 
for  other  repairs  :  how  much  did  it  cost  him  ? 

19.  A  farmer  bought  a  cart  for  thirty-five  dollars, 
a  plough  for  nine  dollars,  and  a  shovel  for  two  dol- 
lars :  what  was  the  cost  of  the  whole  ? 

20.  A  man  bought  a  horse  for  sixty  dollars,  a  sad- 
dle for  ten  dollars,  and  a  bridle  for  three  dollars  : 
how  much  did  he  pay  for  all  ? 

21.  William  boughi  a  i^eography  for  seventy-five 
cents,  a  slate  for  ten  c»^nLs,  a  sponge  fo'  three  cents, 
and  a  lead  pencil  for  two  cents :  what  was  the 
amount  of  his  purchase  ? 

22.  A  farmer  sold  a  horse  and  saddle  for  a  hun 
dred  and  twenty-five  dollars,  which  was  ten  dollars 
less  than  they  cost  him  :  what  did  he  pay  forjLhem? 


SECTION  m. 

S  UBTRACTION. 
LESSON    I. 

1.  Suppose  I  have  two  peaches,  and  give  one  of 
tl;jm  away,  how  many  shall  1  have  left  i 

Solution. — One  peacli  taken  from  two  peaches, 
leaves  one.  Therefore  if  I  have  two  peaches  and  give 
one  of  them  away,  I  shall  have  one  left. 

2.  Open  three  fingers  on  your  left  hand  ;  now  if  you 
shut  ofie  of  thera,  how  many  will  remain  open  ?  Oiie 
taken  from  three  leaves  how  many  ? 

3.  George  having  four  marbles  in  his  hand,  dropped 
one  of  them :  how  many  had  he  left  ? 

iVof«.— The  principle  of  subtracting  one  number  from  another, 
may  be  easily  explained  to  the  pupil  by  the  Numerical  Frame. 
Thua,  to  show  kow  nuvny  three  taken  from  eigkt  will  leave,  move 
across  eight  balls,  then  moving  three  of  thorn  part  way  back,  let 
the  pupil  count  those  that  are  left. 

4.  Leonard  had  five  cents  and  gave  on*,  ^r  a  pen- 
cil :  how  many  cents  had  he  left  ?  One  from  five 
leaves  how  many  ? 

5.  Cornelia  had  fiix  apples  and  gave  one  to  her 
brother :  how  many  had  she  left  ? 

6.  There  are  seven  scholars  belonging  to  this  class ; 
yesterday  one  of  them  was  absent :  how  many  were 
present  ? 

7.  Martha  had  eigkt  roses,  but  on  her  way  to  school 
she  lost  oi^£ :  how  muny  had  she  left  ? 

8.  If  )ou  have  ten  apples,  und  give  away  one  of 
thera,  how  many  wUl     .^u  have  left  ? 


26 

SUBTRACTION.                                                  J! 

SUBTRACTION    TABLE. 

.Vote.— It  U  advisable  tor  the  pupil  to  study  this  Table  in  the  ' 
'  wime  manner  aa  he  did  ths  Addition  Table.    (See  Note,  p.  10.)      t| 

One    from 

one      ie*Te.  naught. 

One       from  six            le>TM  five. 

One      " 

two         "     one. 

One       "     seven       "     six.      ' 

One      " 

threj      •'     two. 

One       "     eight        "     seven,  j 

One       " 

four       "     three. 

One       "     nine         "     eight. 

One       " 

five        •'     four. 

One       "     ten           "      nine. 

Two     from 

two        leare.    naUght. 

Two    frwn  seven     learei  five. 

'  Two      " 

three      "     one. 

Two      "     eight        "     six. 

Two      " 

four             two. 

Two      "     nine         "      seven. 

Two     " 

five        "      three. 

Two      "ten           "      eight,  i 

Two      " 

six        "     four. 

Two      **     eleven     "      nine.    1 

Three  from  three   UaTe.  naught. 

Three  fiora  eight      leavei  five.     ; 

i  Three    " 

four       "     one. 

Three    "     nine      •  "     six. 

Three    " 

five        "     two. 

Three    "     ten           "     seven.  | 

1  Three    " 

six         "     three. 

Three   "     eleven     "     eight.    | 

!  Three    " 

seven    *'     four. 

Three   "     twelve     "     nine.    ! 

i    Four     from 

four     it*rs»  naught. 

Four    from   nine          lea»et  five.       1 

i  Four    « 

five        '■     one. 

Four     "ten            "      six.      | 

!  Four    " 

six         "     two. 

Four     "     eleven      "     seven,  i 

Four    " 

seven     "      three. 

Four     "     twelve      "     eight.    , 

i  Four    " 

eight       "     four. 

Four    "     thirteen    "      nine.    | 

;    Five     'rom 

five      leiTM  naught. 

Five    from  'en         iea»e.  five. 

Five     " 
!  Five     " 

six          "      one. 

Five      "     eleven      "      six. 

seven     "      two. 

Five      "     twelve      "     seven   i 

Five     " 

eight      "     three. 

Five      **     thirteen    •'     eight    1 

Five     " 

nine       '*     four. 

Five      "     fourteen  "     nine.     ■ 

;    Six        fnw. 

six        iea»et  naught.  j  Six      from  eleven    itaT«t  five. 

Six       " 

seven     "     one.        j  Six       "     twelve      "     six.      j 

i   Six         " 

eight      "     two.          Six       "     thirteen    "     seven.  '. 

1  Six       " 

nine       "     t  iree.        Six       "     fourteen   "     eight.  | 

Six        ' 

ten         "     fom.         Six       *«     fifteen       "      nine,    i 

SUBTRACTION. 


27 


.-  I 


Seven 

from  seven 

leares  naUght. 

Seven  from  twelve    leare 

five. 

Seven 

"   eight 

"     one. 

Seven    "   thirteen   " 

six. 

Seven 

"   nine 

"    two. 

Seven    "   fourteen  " 

seven. 

Seven 

"   ten 

"     three. 

Seven    "   &iieen      " 

eight. 

Seven 

•'   eleven 

"     four. 

Seven    "  sixteen     " 

nine. 

Eight 

row  eight 

leaTM  naught. 

Eight  from  thirteen  ieaTe«five. 

Eight 

"   nine 

"    one. 

Eight     •'   fourteen   " 

six. 

Eight 

"   ten 

"    two. 

Eight     "   tifteen      " 

seven 

Eight 

"   eleven 

"     three. 

Eight     "    sixiean     " 

eight 

Eight 

"   twelve 

"     four. 

Eight     "  seventeen " 

nine. 

Nine 
Nine 
Nine 
Nine 
Nine 


trom  nine         leares 

•'  ten  " 

■*  eleven  " 

'•  twelve  " 

"  thirteen  " 


naught. 

one. 

two. 

three. 

four. 


Nine 
Nine 
Nine 
Nine 
Nine 


fruiu  fourteen  leav«. 

"  fifteen       " 

"  sixteen      " 

'*  seventeen  " 

"  eighteen    " 


five. 

six. 

seven 

eight. 

nine. 


LESSON    I 


1.  William  had  two  apples  when  he  started  from 
home,  and  has  given  two  away :  how  many  has  he 
rn)\v  I     Two  from  two  leaves  how  many  ? 

2.  Eliza  had  four  cents,  and  has  spent  two  of  them 
for  candy :  how  many  cents  has  she  left  ? 

Note. — The  pupil  should  think  what  number  added  to  two 
makes  four,  and  that  will  be  the  number  of  cents  she  now  has. 

3.  There  were  three  doves  upon  the  roof  of  a 
barn,  but  two  of  them  have  flown  away :  how  many 
remain  upon  the  roof?  Two  from  three  leaves  how 
many  ?     One  from  three  leaves  how  many  ? 

4.  Marbles  were  formerly  five  cents  a  dozen,  but 
now  they  are  two  cents  cheaper  :  what  do  they  now 
cost  a  dozen?  Two  and  what  number  make  five? 
Three  from  five  leaves  how  many  ? 

5.  Joseph  having  seven  cents,  gave  two  of  them 


29 


SUBTRACTION. 


for  a  peach  :  how  many  cents  had  he  left?  Two 
and  what  number  make  seven  ?  Five  from  seven 
leaves  how  many  ? 

6.  A  boy  bou«Tht  six  tumblers,  and  broke  two  of 
them  in  carrj'ing  them  home;  how  many  whole 
ones  were  left  ?  Two  and  what  number  make  six  ? 
Four  from  six  leaves  how  many  1 

7.  Formerly  there  were  nine  shade  trees  in  front 
of  the  school  house,  but  two  have  been  cut  down  : 
how  many  remain  ? 

8.  There  are  eight  scholars  in  the  Geography 
class ;  two  of  them  missing  their  lesson,  were  de- 
tained :  how  many  were  permitted  to  take  their 
seats  ? 

9.  A  boy  having  ten  rabbits,  lost  two  of  them  : 
how  many  had  he  left  ?  7\vo  and  what  number 
make  ten  ?     Eight  from  ten  leaves  liow  many  ? 


LESSON  in 

1.  Edwin  nad  three  oranges,  and  gave  each  of  his 
three  sisters  one  apiece  :  how  many  had  he  left  i 
Three  from  three  leaves  how  many  ? 

2.  If  Edwin  had  four  oranges,  and  should  flfive 
away  three,  how  many  would  he  have  left?  I'Lee 
from  four  leaves  how  many  ? 

8.   A  boy  was  sent  to  buy  six  eggs,  by  careless- 
ness he  broke  three  of  them:  how  many  whole  ones  ij 
had  he  left  ?     Three  and  what  number  make  six  ?     :| 

4.  A  man  put  five  cows  in  a  pasture,  but  .nree 
of  them  jumped  out :  how  many  remained  in  the 
pasture  ? 

5.  Louisa  havin^r  seven  shillings,  gave  three  of 


SUBTRACTION.  29 


them  for  a  pair  of  gloves  :  how  many  shillings  had 
she  then  ? 

6.  Frank  had  nine  chickens,  but  three  of  them 
were  kille«i  by  the  hawks :  how  many  had  he  left  ? 

7.  Eight  boys  were  permitted  to  go  out,  but  only 
tkree  of  them  chose  to  go :  how  many  staid  ir. 
school  ? 

8.  Eleven  boys  were  called  up  to  be  punished  for 
bad  conduct,  all  but  three  of  them  confessed  and 
were  pardoned :  how  many  escaped  the  punish- 
ment ? 

9.  Julia  finding  ten  roses  on  her  bush,  picked  off 
three :  how  many  remained  on  the  bush  ? 

10.  There  were  twelve  peaches  in  a  fruit  basket, 
three  of  which  had  begun  to  decay  :  how  many 
sound  ones  were  there  I 

LESSON  IV. 

1.  Joseph  having  five  lemons,  gave  foui  of  them 
for  a  knife :  how  many  had  iie  left  ? 

2.  There  were  seven  chairs  in  a  school  room, 
four  of  which  were  bioken  :  how  many  whole  ones 
were  there  ? 

'3.  Mary  having  six  pears,  gave  four  of  them  to 
her  brothers :  how  many  had  she  left  ? 

4.  On  a  training  day,  nine  boys  formed  themselves 
into  a  military  company,  four  of  them  were  officers 
and  the  remainder  were  privates:  how  many  pri- 
vates were  there  ? 

5.  John  made  eight  marks  on  his  sla*e,  and  then 
rubbed  out  four  of  them  :  how  many  marks  remain- 
ed ? 

6.  A  pouni  of  sugar  is  worth  tep  *»nta,  and  a 


30  SUBTRACTION, 


quart  of  vinegar  is  worth  four  cents:  hrf)W   much 
more  is  the  sugar  worth  than  the  vinegar  ? 

7.  Lucretia  had  twelve  flower  pots  standing  ic  the 
window,  and  four  of  them  fell  out :  how  many  re- 
mained in  the  window  ? 

8.  Edward  exchanged  his  kite  worth  eleven  ceuts 
for  an  inkstand  worth  four  cents,  and  received  the 
balance   in   money  :  how   much   money  did   he  re 
ceive  ? 

9.  William  gave  thirteen  cents  for  a  slate,  and 
four  cents  for  a  sponge  :  how  much  more  did  his 
slate  cost  than  his  sponge  ? 

10.  There  are  fourteen  pages  in  Henrietta's  wri- 
ting-book, and  she  has  written  four  of  them :  how 
many  pages  remais  to  be  written  ? 

LESSON    V. 

1.  If  an  orange  costs  six  cents,  and  a  lemon  costs 
five  cents,  how  much  more  does  an  orange  cost  than 
a  lemon  ? 

2.  A   man  having  bought  eight  yards  of  cloth. 
,  used  five  yards  to  make  a  suit  of  clothes :  how  many 

yards  had  he  left  ? 

3.  Frank  has  seven  marbles,  and  John  has  five  : 
how  many  more  marbles  has  Frank  than  John  ? 

4.  A  man  bought  a  cow  for  ten  dollars,  and  gave  j 
a  barrel  of  flour  worth  five  dollars,  and  paid  the  rest 
in  money  :  how  much  money  did  he  pay  ? 

5.  If  a  bushel  of  wheat  costs  nine  shillirjgs,  and  a 
bushel  of  corn  five  shillings,  what  is  the  difference 
in  their  price  ? 

6.  A  man  bought  a  quantity  of  butter  for  twelve 
dollars,  but  finding  it  damaged,  sold  it  for  five  dol- 


SVBTRACTION.  31 


lars  less  than  he  gave  for  it :  for  how  much  did  he 
sell  it  ? 

7.  If  you  had  eleven  dollars  and  should  pay  five 
dollars  for  a  hat,  how  many  dollars  would  you  have 
left? 

I  8.  John  answered  thirteen  questions  and  Peter 
only  five :  how  many  more  questions  did  John  an- 
swer than  Peter  ?  4> 

9.  A  trader  bought  a  keg  of  tobacco  for  fourteen 
dollars,  and  sold  it  for  five  dollars  less  than  he  gave  : 
how  much  did  he  sell  it  for  ? 


LESSON   VI. 

1.  There  were  seven  passengers  in  a  stage,  six  of 
whom  got  out :  how  many  were  left  in  the  stage  ? 

2.  George  bought  nine  quills,  and  used  up  six  of 
them  in  a  week  :  how  many  had  he  left  ? 

3.  A  boy  liaving  eight  cents,  bought  six  cents 
worth  of  figs  :  how  many  cents  had  he  left  ? 

4.  Jane  having  eleven  walnuts,  cracked  bix  of 
them  :  how  many  whole  ones  has  she  ? 

5.  Moses  sold  his  knife  for  ten  cents,  which  vvas 
six  cents  more  than  he  gave  for  it :  how  much  did  it 
cost  him  ? 

6.  A  writing-book  costs  thirteen  cents,  and  an 
inkstand  six  cents :  how  much  more  must  I  pay  for 
a  writing-book  than  an  inkstand  ? 

7.  Harriet  bought  twelve  knots  of  yarn,  and  used 
six  knots  in  knitting  herself  a  pair  of  stockings  :  how 
many  knots  had  she  left  ? 

j      8.  During  the  last  fourteen  days  it  has  rained  six 
days :  how  many  fair  days  have  there  been  ?     Eight 
I  from  fourteen  leaves  how  many  ? 


32  SUBTRACTION. 


9.  A  watermelon  costs  fifteen  cents,  and  a  musk- 
melon  six  cents :  what  is  the  difference  in  their 
prices  ? 

LESSON   Vll 

1.  Sarah  had  eight  pins,  but  she  has  lost  seven  of 
them  :  how  many  has  she  left  ? 

2.  Catharine  having  a  present  of  nine  peachea, 
gave  away  seven  of  them,  and  kept  the  remainder : 
how  many  did  she  keep  ? 

3.  Seven  from  eleven  leaves  how  many  ?  Four 
from  eleven  leaves  how  many  ? 

4.  A  merchant  had  ten  yards  of  cloth  in  a  piece, 
and  sold  seven  yards  of  it ;  how  many  yards  were 
left? 

5.  If  you  had  twelve  apples  and  should  give 
away  seven  of  them,  how  many  would  you  have 
left? 

6.  John  had  thirteen  marbles  and  lost  seven  of 
them  at  play  •  how  many  had  he  left  ? 

7.  A  farm"  drove  fourteen  sheep  to  market,  but 
could  sell  01  dy  seven  of  them  :  how  many  had  he 
left  ? 

8.  Seven  from  sixteen  leaves  how  many  ?  Nine 
from  sixteen  leaves  how  many  ? 

9.  A  man  bought  a  keg  of  molasses  containing 
fifteen  gallons,  and  having    used  a  quantity  of  it, 

I  found  he  had  seven  gallons  left :  how  much  nad  he 
used  ? 

10.  There  were  seventeen  caps  hung  up  in  the 
entry,  but  during  recess  seven  of  them  were  knocked 
down  :  how  many  of  them  were  left  hanging  ?  Ten 
from  seventeen  leaves  how  many  ? 


SUBTRACTION. 


LESSON    VIII. 

1.  Frank  bought  a  book  for  eight  cents,  and  sod 
I  it  for  eleven  cents :  how  much  did  he  make  by  his 

bargain  ? 

2.  A  lady  bought  a  dress  for  eight  dollars,  and 
handed  the  shopkeeper  a  ten-dollar  bill :  how  much 
chanjje  ought  she  to  receive  back  ? 

3.  John  bought  a  sled  for  nine  cents,  and  paid 
eight  cents  down :  how  many  cents  does  he  still 
owe  for  it  ? 

4.  There  are  twelve  weeks  in  a  quarter,  and 
eight  of  them  are  past :  how  many  weeks  before  the 
quarter  will  end  ? 

5.  Eight  Trom  fifteen  leaves  how  many  ?  Seven 
fiom  fifteen,  how  many  ? 

6.  Ei<rht  from  thirteen  leaves  how  many  ?  Five 
from  thirteen,  how  many  ? 

7.  Margaret's  vacation  is  fourteen  days  long,  and 
she  has  been  at  home  eight  days :  how  many  days 
before  she  must  return  to  school  ?  Eight  from 
fourteen  leaves  how  many  ? 

8.  A  boy  having  sixteen  oranges  in  his  basket, 
sold  eight  of  them  to  the  Railroad  passengers :  how 
many  has  he  left  ? 

9.  A  little  girl  went  a  shopping  with  seventeen 
cents  in  her  purse,  and  on  her  j^eturn,  found  she  had 
eight  cents  left :  how  much  did  she  spend  ?  Eight 
from  seventeen  leaves  how  many  ? 

10.  A  man  selling  a  cow  for  eighteen  dollars,  took 
eight  dollars  hi  goods  and  the  rest  in  money :  how 
much  money  did  he  receive  ?  Eight  from  eighteen 
leaves  how  many  ? 


34  SUBTRACTION. 


LESSON    IX. 

1  -  If  )  ou  buy  a  pound  of  sugar  for  nine  cents, 
and  give  the  shopkeeper  a  ten-cent  piece,  how  much 
change  ought  he  to  give  you  ? 

2.  In  the  Algebra  class  there  are  twelve  schol- 
ars, and  nine  of  them  recited  their  lesson  perfectly  ; 
how  many  failed  ?  Three  from  twelve  leaves  how 
many  ? 

3.  Susan  has  eleven  pmks  and  nine  tulips :  how 
many  tulips  must  she  receive  to*make  them  equal 
in  number  to  her  pinks  ?  Two  from  eleven  leaves 
how  many  ? 

4.  Harriet's  age  is  thirteen  years,  and  Lucy's  is 
nine  years:  how  much  older  is  Harriet ^han  Lucy? 
Four  from  thirteen  leaves  how  many  ? 

5.  Nine  from  fifteen  leaves  how  many  ?  Six 
from  fifteen,  how  many  ? 

6.  Nine  from  fourteen  leaves  how  many  ?  Five 
from  fourteen,  how  many  ? 

7.  Albert  has  sixteen  plums,  and  James  nine : 
'  how  many  must  James  receive  to  make  his  number 
i  equal  to  that  of  Albert  ? 

I       8.  A  merchant  bought  a  quantity  of  beef  at  sev- 
I  enteen  dollars  a  barrel,  and  finding  it  damaged,  sold 
I  it  for  nine  dollars  a  barrel ;  how  much  did  he  lo 
>  on  a  barrel  ? 

j       9.   William  had  eighteen  cents  in  his  pocket,  and 
'  on  h.'s  way  to  school  he  spent  nine  of    hem :  how 

many  cents  had  he  left? 

10.  in  school  street  there  are  nineteen  shade  trees, 

nine  of  which  are  elms,  and  the  rest  are  maples : 

how  many  maple  trees  are  there  ? 


SUBTRACTION.  35 


1.ESS0N    X* 

1.  One  from  ten  leaves  how  many?  One  fir«i 
twenty  ?  One  from  thirty  ?  One  from  forty  1  One 
from  seventy  ?  One  from  sixty  ?  One  from  eighty  ? 
One  from  fifty  ?  One  from  ninety  ?  One  from  a 
hundred  ? 

2.  Two  from  ten  leaves  how  many  ?  Two  from 
twenty  ?  Two  from  thirty  ?  Two  from  forty  ?  Two 
from  sixty  ?  Two  from  eighty  ?  Two  from  fifty  ? 
Two  from  seventy  ?  Two  from  ninety  ?  Two  from 
a  hundred  ? 

3.  Four  from  ten  leaves  how  many  ?  Four  frori 
twenty  1  Four  from  thirty  ?  Four  from  sixty  1  Four 
from  forty?  Four  from  fifty?  Four  from  ninety? 
Four  from  seventy  ?  Four  from  eighty  ?  F'our  from 
a  hundred  ? 

4.  Three  from  a  ^hundred  leaves  how  -many  ? 
Three  from  ninety  ?  Three  from  eighty  ?  Three 
from  seventy  ?  Three  from  sixty  ?  Three  from  fifty  ? 
Three  from  forty  ?  Three  from  thirty  ?  Three  from 
twenty  ?  '  'Three  from  ten  ? 

5.  Five  from  a  hundred  leaves,  how  many  ?  Five 
from  ninety "?  From  eiglUy  ?  Seventy?  Sixty? 
Fifiy  ?  Forty  ?  Thirty  ?  Twenty  ? 

6.  Six  from  fourteen  leaves  how  many  ?  Six  from 
Twenty?  From  thirty  ?  Fifty?  Forty?  Sixty? 
Eighty?  Ninety?  Seventy?  A  hundred? 

7.  Seven  tVom  ten  leaves  how  many  ?  Seven  from 
Twenty  ?  From  forty  ?  Thirty  ?  Seventy  ?  Sixty  ? 
Eighty  ?  Fifty  ?  Ninety  ?  A  hundred  ? 

*  Th^i  pupil  should  be  able  to  answer  the  questions  in  tliis  and  the 
following  I>efl9on,  with  readiness,  before  he  proceeds  to  tlie  next. 


36  SUBTRACTION. 


8.  Eight  trom  ten  leaves  how  many  ?  Eight  from 
twenty  f  From  thirty  ?  Fifty  ?  Forty  ?  Sixty  ? 
Eighty  ?  Seventy  ?  Ninety  ?  A  hundred  ? 

9.  Nine  from  ten  leaves  how  many  ?     Nine  from 
twenty  ?  From  forty  ?   Eighty  ?  Ninety  ?  Seventy  ?  ' 
Fifty?  Sixty?  Thirty?  A  hundred?  | 

LESSON    XJ 

1.  Ten  from  twelve  leaves  how  many  ?  Ten  from 
twenty-three  ?  Ten  from  thirly-four  ?  Ten  from  for- 
ty-five  ?  Ten  from  fifty-six  ?  Ten  from  sixty-seven  ? 
Ten  from  seventy-eight  ?  Ten  from  eighty-nine  ? 
Ten  from  a  hundred  ? 

2.  Five  from  twelve  leaves  how  many  ?  Five 
from  twenty-two  ?  Five  from  thirty-two  ?  Five  from 
sixty-two  ?  Five  from  forty-two  ?  Five  from  seven- 
ty-two? Five  from  fifty-two?  Five  from  eighty-two? 
Five  from  ninety-two  ? 

3.  Three  from  eight  leaves  how  many  ?  Three 
from  eighteen  ?  Three  from  twenty-eight  ?  Three 
from  fifty-eight  ?  Three  from  forty-eight  ?  Three 
from  sixty-eight  ?  Three  from  thirty-eight  ?  Three 
from  seventy-eight  ?  Three  from  ninety-eight  ? 
Three  from  eighty-eight  ? 

4.  Four  from  nine  leaves  how  many  ?  Four  from 
nineteen  ?  Four  from  thirty-nine  ?  Four  from  twen- 
ty-nine ?  Four  from  sixty-nine  ?   Four  from  seventy- 

'  nine  ?  Four  from  fifty -nine  ?  Four  from  forty-nin«  ? 
j  Four  from  eighty-nine  ?  Four  from  ninety-nine  ? 

5.  Six  frDm  seventeen  leaves  how  many  ?  Six 
from  twenty-eight  ?  Six  from  fifty-four?  Six  from 
thirty-eight  ?     Six  from  eighty-seven  ? 

6.  Seven    from   twenty- five   leaves  h  >w  many  ? 


SUBTRACTION.  37 


Seven  from  forty-nine  "^  Seven  from  thirty-six  ? 
Seven  from  sixcy-three  ?  Seven  from  eighty-lour  t 
Seven  from  ninety-eight  ? 

LESSON  XII. 

1.  A  mm  boii<:ht  a  cow  for  ten  dollars,  and  sold 
I  it  a<rain  for  twelve  dollars  :  how  much  did  he  make 
;  by  his  bariiain  ?  Ten  from  twelve  leaves  liow 
j  many  ?  Two  from  twelve,  how  many  ? 
I  2.  Ten  from  eleven  leavers  how  many  ?  One 
I  from  eleven,  how  many  ? 

!       3.   William's  x\rithmetic  lesson  contained  thirteen 
I  questions,  and  he  rociied  ten  of  them  perfectly  :  how  j 
I  many  did  he  miss  ?    . 

I  4.  Charles  paid  fifteen  cents  for  a  knife,  and  sold 
I  it  for  ten  cents :  how  much  did  he  lose  by  his  bar- 
1  gain  ? 

j  5.  A  robber  was  sentenced  to  the  State's  prison 
!  for  fourteen  years,  and  after  ten  years  had  elapsed 
I  he  was  pardoned  out :  how  many  years  of  his  sen- 
I  tence  still  remained  ? 

:       6.   A  lady  vvent  a  shopping  with  sixteen   dollars 
in  her  purse,  and  having  paid  ten  dollars  for  a  dress, 
gave  ihe  rest  for  a  bonnet :  what  was  the  price  of 
'  the  bonnet  ? 

7.  Heniy  having  eighteen  canary  birds,  wishes 
to  keep  ten  of  them  and  sell  the  remainder  :  how 
i  many  can  he  sell  ? 

I  8.  Ten  from  seventeen  leaves  how  many  ^  Seven 
I  from  seventeen,  how  many  ? 

■       9.  In  an  orchard  containing  nineteen  trees,  ten  of 
I  them  are  apple-trees,  and  the  rest  are  peach  treea :  [ 
I  how  many  peach-trees  are  there  ? 


can  the  car  go/than  tie  Wse  »"  """"^ ""-«  ""il- 
yards  did  he  hat;  ?eft  f    ^'""^''  ^^^^^^  •  ^ow  many  I 
LESSON   XIII. 

^-.  It  is  called  S.U.IZ^"^''"  been  solved?  / 
^;fg^^'"'ti^S"I>traction?  I 

subu£til?eii;:dt  "'"""■  •"■ ""»''«'  °*'-wby  I 

^-  What  is  the  (^Irenct ,.  f ""'"  -^'^  ^'^i  '""« ? 

a  Kron,  twenty  aubrct  Ltr  ^"  ^"<^  "^"•'-' '  I 
10^-  J,,'""" 'i^Wy-five  subtract  si 
10.  i  rom  6«y.ti.,,e  take  ten.  I 

1.  hrom  forty-se.en  tate  four. 


SUBTRACTION.  39 


EXAMFLES    FOR    IRACTICE. 

1.  James  gave  twelve  cents  for  a  quart  of  cher- 
ries, and  eight  cents  for  a  quart  of  chestnuts  :  how  ' 
much  more  did  he  pay  for  his  cherries  than  for  his  I 
chestnuts?  ! 

2.  A  man  gave  seventeen  dollars  for  a  cow,  and  j 
nine  dollars  for  a  load  of  hay  :  how  much  more  did  I 
he  give  ihr  the  cow  than  for  the  hay  ?  ] 

3.  Horace  having  thirty-six  marhles,  gave  ten  to  j 
his  cousin  :  how  many  had  he  left  I 

4.  Susan  had  twenty. four  peaches;  she  gave  six  I 
to  Harriet,  and  four  to  Ann  :  how  many  peaches  had  i 
she  left  ? 

5.  On  a  training  day  a  little  boy  had  fifty  cents ; 
he  spent  ten  cents  for  pea-nuts  and  lost  five  cents : 
how  many  cents  had  he  lefl  ? 

6.  A  man  bought  a  wagon  for  th:rty.six  dollars, 
and  sold  it  for  ten  dollars  less  than  cost :  how  nmch 
did  he  get  for  it  ? 

7.  A  merchant  bought  a  hogshead  of  molasses 
containing  sixty-three  gallons,  and  found  that  eight 
gallons  had  leaked  out:  how  many  gallons  were 
left  ? 

8.  A  barrel  of  brandy  cc«ts  twentv-nine  dollars, 
and  a  barrel  of  flour  costs  six  CK.jt  k  vhat  is  the 
difference  in  their  price  ? 

9.  The  cost  of  a  cloak  is  forty-five  dollars,  and 
the  cost  of  a  hat  eight  dollars:  what  is  the  differ- 
ence  in  their  cost  ? 

10.  A  man  bought  a  horse  for  seventy-five  dollars, 
and  sold  it  for  ton  dollars  less  than  he  paid  :  how 
much  did  he  get  fcTr  his  horse  ? 


40  SUBTRACTION. 


11.  Samuel  is  nineteen  years  old,  and  his  sister  is 
six  years  younger :  how  old  is  she  ? 

12.  The  cost  of  an  Arithmetic  is  twenty-five  cents, 
and  the  cost  of  a  slate  is  twenty  cents :  what  is  the 
difference  in  their  cost  ? 

18.  Henry  having  thirty-six  marbles,  lost  six  and 
gave  away  five :  how  many  had  he  left  ? 

14.  George  having  twenty-eight  apples,  gave  three 
to  one  companion,  two  to  another,  and  four  to  an- 
other:  how  many  had  he  left? 

15.  A  man  bought  a  sleigh  for  twenty  dollars  and 
paid  ten  dollars  ibr  painting  it ;  he  then  sold  it  for 
thirty-two  dollars:  did  he  make  or  lose  by  the  bar- 
gain ?     How  much  ? 

16.  A  man  owning  forty  acres  of  land,  sold  twenty 
acres  of  it:  how  many  acres  had    he  left  ? 

17.  Henry's  kite  line  is  fifty  yards  long,  and  Wil. 
liam's  is  forty  yards  long :  what  is  the  dillerence  in 
their  length  ? 

18.  A  farmer  having  a  hundred  bushels  of  wheat, 
sold  fifty  bushels  :  how  many  bushels  had  he  left  ? 

19.  If  I  have  seventy-five  cents,  and  give  ten  to 
Charles,  six  to  James,  four  to  Susan,  and  six  to 
Harriet,  how  many  cents  shall  I  have  left? 

20.  If  you  have  fifty  peaches,  and  give  ten  to  one 
com[)anion,  ten  to  a  second,  ten  to  a  third,  and  ten 
to  a  fourth,  how  many  peaches  will  you  have  lefl  ? 

21.  George  having  twenty -one  marbles  lo«*t  eight  of 
them,  and  afterwards  gained  twelve :  how  many  did  I 
he  then  have  ?  ; 

22.  Sarah  has  twelve  roses,  Mary  has  five  less^  than  ' 
Sarah,  and  Susan  three  less  than  Mary :  bow  many  | 
have  all  ?  j 

23.  If  you  take  sixteen  from  twenty,  and  add  twen- ! 
ty-five  to  the  remainder,  what  will  the  sum  be !  i 


SECTION   IV 
MULTIPLICATION. 

LESSON    I. 

^.  What  will  two  apples  cost,  at  one  cent  apiece  ? 

Solutio-n. — If  one  apple  costs  one  cent,  two  apples 
w  11  cost  two  times  one  cent :  and  two  times  one  cent 
ar3  two  cents.     Ans.  Two  cents. 

2.  What  will  two  pears  cost,  at  two  cents  apiece  ? 

Note. — The  learner  should  be  required  to  give  the  reaaoning  in 
the  solution  of  every  example. 

3.  At  three  cents  a  yard,  what  will  two  yards  of 
ribbon  cost  ? 

4.  At  four  cents  apiece,  what  will  two  oranges 
come  to  ? 

5.  George  bought  two  melons,  at  five  cents  apiece  : 
how  much  did  he  pay  for  them  ? 

6.  if  one  lemon  is  worth  six  cents,  how  many 
cents  are  two  lemons  worth  ? 

7.  What  will  two  muffs  cost,  at  seven  dollars 
apiece  ? 

8.  What  cost  two  quarts  of  cherries,  at  eight  cents 
j  a  quart  ? 

9.  At  nine  cents  a  pound,  \''hat  will  two  pounds 
I  of  sugar  cost  ? 

Note  — The  principle  of  miiW/jZymg cannot  be  loo  carefully  ex- 
plained to  young  pupils.  To  show  ihem,  for  eiainple,  that  tvo 
times  ten  are  twenty,  move  out  ten  balls  on  one  cf  the  wires  of  the 
iNuraerical  Frame,  tlien  move  out  tew  on  anolhei  wire  and  let  him 
liim  '".ouut  these  two  tens  togetht>r. 

While  learning  the  Muliiplication  Table,  the  ;lass  may  study 
to  advantage  the  Lessons  corresponding  with  its  different  parts, 
as  in  Addition  and  Subtraction. 


j 

1   43                                      MULTIPLICATION. 

1 

MULTIPLICATION     TABLE. 

Two     timet  One     are  tWO. 

Two      Ume.  six      are  twelve. 

Two      "    two    "  four. 

Two      "    seven "  fourteen. 

Two      "    three  "  six. 

Two       "    eight  "  sixteen,     j    ' 

1  Two      "    four  "  eight. 

Two       "    nine  "  eighteen. 

^  Two      ''    five    "  ten. 

Two       "ten      "  twenty. 

Three  time,  one    are  three. 

Three  Ume.  six    are  eighteen. 

j  Three   "    two     "  six. 

Three     "    seven"  twenty-one.  ' 

i  Three   "    three  «'  nine. 

Three     "    eight  "  twenty-four. 

Three   "    four    "  twelve. 

Three     "    nine  "  twenty-«uir. 

Three   "    five     "  fifteen. 

Three    "    ten     "  thirty. 

Pour  timM  one    are  four. 

Four    time,  six    are  twenty-four. 

!  Four     "    two    "  eight. 

Four      **    seven "  twenty-ei^ht. 

Four     •'    three  "  twelve. 

Four      "    eight  "  thirty-two. 

Four     "    four    "  sixteen. 

Four      "    nine  "  thirty-sir 

Four     "    five    "  twenty. 

Four      "    ten     "  forty. 

P'ive     timeiOne    are  five. 

Five     limes  six    are  thirty. 

Five      "    two    "  ten. 

Five       "    seven"  thirty- five 

Five      "    three  "  fifteen. 

Five       "    eight  "  forty. 

Five      "    four   "  twenty. 

Five       "    nine   "  forty-five. 

Five       "    five    "  twenty-five. 

Five       "    ten      "  fifty. 

Six        time,  one     are  SIX. 

Six       ime.  six     are  thirty-six. 

Six        "    two    "  twelve. 

Six        "    seven "  forty-two.       ( 

Six        "    three  "  eighteen. 

Six        "    eight  "  forty-eight 

Six        "    four    "  twenty-four. 

Six        "    nine   "  fifty-four.  >, 

Six         =    fiTe    "  thirty. 

Six        "    ten      "  sixty. 

Seven  iin»e«  one  are  seven. 
Seven    "    two    "  fourteen. 
Seven    "    three"  twenty -one. 
Seven    "    four  "  twenty-eight. 
Seven    "    five   "  thirty-five. 


Seven  time,  six    ar«  forty-two. 
Seven   "    seven  "  forty-nine. 
Seven   "    eight  "  fifty-six. 
Seven   "    nine  "  sixiy-three 
Seven   "    ten      "  sf  "enty. 


MULTIPLICATION. 


43 


'  Eight  time*  one    aw  eight 
Eight    "   two     "  sixteen. 


Eight 
Eight 
Eight 
Nine 
Nine 
Nine 
Nine 
Nine 


three   "  twenty- fou. 
four     "  thirty-two, 
live      "  forty. 


I  Eight  tirae.  six     M«  forty-eight. 
Eight     "  seven  "  fifty-six. 
Eight    "  eight  "  eixty-four. 


one    are  nine, 
two     "  eighteen, 
three   "  twenty -sev, 
four    "  thirty-six. 
five      "  forty-five. 


Eight 
Eight 


nine    "  seventy-two. 
ten      "  eighty. 


Nine  time,  six      «« fifty- four. 
Nine     *'   seven  "  sixty-three. 
Nine     "   eight    "  seventy-two. 
Nine      "    nine     '*  eighiy-one. 
Nine      "   ten       "  ninety. 


Ten  u»»»M  one    are  ten.  Ten  umo*  six      are  sixty. 

Ten       "   two      "  twenty.  Ten       "   seven  "  seventy. 

Ten       "  three   "  thirty.  Ten      "   eight    "  eighty. 

Ten       "   four     "  forty.  Ten       "   nine     "  ninety. 

Ten       "   five      "  fifty.  Ten       "   ten       '•  one  hundred. 

Note. — It  is  an  interesting  and  profita})le  exercise,  for  yoimg 
pupils,  to  recite  tables  in  concert.  But  it  will  not  do  to  depend 
'jpon  this  method  al»ne.  It  is  indisprasable  for  every  scholar  who 
desires  to  be  accurate  either  in  arithmetic  or  business,  to  have  the 
cfinmon  arithmetical  tables  distinctly  and  indtlihlif  fixed  in  \\\» 
.n'ii«i.  Hctice,  after  a  table  has  been  repealed  by  the  class  in 
oor  Tiert,  or  individually,  the  Teacher  should  ask  many  prorais- 
e^oua  questions,  to  prevent  its  being  recited  mechanically,  [rota 
a  knowledge  of  the  regular  increase  of  numbers. 

LESSON     II. 

1.  What  will  three  quarts  of  strawberries  cost,  at 
one  shilling  a  quart  ? 

2.  At  two  cents  apiece,  what  will  three  lead  pen- 
cils come  to  ? 

3.  In  one  yard  there  are  tlnoc  ieet :  how  many 
feet  are  there  in  three  yards  ? 

4.  At  four  cents  apiece,  what  will  three  oranges 
cost  ? 

5.  What  cost  three  quarts  of  milk,  at  five  cents  a 
quart  ? 


44  MULTIPLICATION . 


6.  What  cost  three  ounces  of  snufT,  at  six  cents 
an  ounce  ? 

7.  At  seven  cents  a  pound,  what  will  three  pounds 
of  cheese  come  to  ? 

8.  In  one  peek  there  are  eight  quarts  :  how  many 
quarts  are  there  in  three  pecks? 

9.  If  it  requires  nine  yards  of  calico  to  make  one 
dress,  how  many  yards  will  it  require  to  make  three 
d'2sses? 

10.  A  man  gave  three  boys  ten  apples  apiece  : 
how  many  did  he  give  them  all  ? 

LESSON    III. 

1.  At  one  dollar  a  bushel,  how  much  will  four 
bushels  of  wheat  cost  ? 

2.  What  cost  four  lemons,  at  two  cents  apiece  ? 

3.  If  Frederic  obtains  four  credit  marks  a  day, 
how  many  will  he  have  in  four  days? 

4.  What  cost  four  quarts  of  cider,  at  three  cents  a 
quart  ? 

5.  Jane  bought  four  skeins  of  sewing  silk,  at  five 
cents  a  skein  :  how  much  did  she  piy  for  them  all?.j 

6.  In  one  week  there  are  seven  days  :  how  many 
days  are  there  in  four  weeks? 

7.  Henry  had  four  class-mates,  and  gave  them  six 
apples  apiece  :   how  many  did  he  give  to  all  ? 

8.  What  cost  four  hats,  at  nine  dollars  apiece  ? 

9.  Wha  cost  four  barrels  of  flour,  at  eight  dollar*  | 
a  barrel  ? 

10.  At  ten  dollars  a  ton,  what  wi.l  four  tons  of 
hay  cost? 


MrLTTILJCATTON.  45 

I 

LESSON    IV. 

1.  At  one  do  lar  a  yard,  what  will  five  yards  ol 
gilk  cost  ? 

2.  What  cost  five  lemons,  at  three  cents  apiece  ? 

3.  My  board  costs  me  two  dollars  a  week  :  what 
will  it  amount  to  in  five  weeks  ? 

4.  A  man  hired  a  horse  for  six  cents  a  mile  :  how 
much  must  he  pay  for  going  five  miles  1 

5.  Saralj's  cloak  contains  five  yards  of  merino, 
whic.i  cost  five  shillings  a  yard  :  how  much  did  hei 
cloak  cost  ? 

6.  What  cost  five  pair  of  boots,  at  four  dollars  a 
pair? 

7.  I'^ight  quarts  make  one  peck  :  how  many  quarts 
are  there  in  five  pecks  ? 

8.  If  a  stage  goes  seven  miles  an  kour.  how  far 
will  it  go  in  five  hours? 

9.  At  nine  cents  a  pound,  what  will  five  pounds 
of  butter  cost  ? 

10.  ^Vhat  cost  five  yards  of  cloth,  at  tei  shillings 
a  yard  ? 

LESSON    V. 

1.  What  cost  six  yards  of  calico,  at  one  shilling  a 
yard  ? 

2.  What  cost  six  oranges,  at  three  cents  apiece? 

3.  There  are  four  weeks  in  a  month ;  how  many 
weeks  are  there  in  six  months  1 

4.  What  cost  six  yards  of  cloth,  at  two  dollars  a 
yard  ? 

5.  What  cost  six  spools  of  cotton,  at  five  cents  a 
spool  ? 


46  MULTIPLICATION. 


6.  At  seven  cents  a  pound,  what  will   a  quarter  I 
ol  Iamb  weighing  six  peunds,  come  to  ?  I 

7.  What  cost  six  quarts  of  plums,  at  ten  cents  a  ! 
quart  ?  I 

8.  Sarah   bought  six  yards  of  ribbon,   at  seven  ! 
cents  a  yard  :  how  much  did  she  pay  for  it  ?  ! 

9.  If  one  inkstand  costs  six  cents,  how  much  will  | 
six  ccsl  ?  I 

10.  What  cost  six  pounds  of  raisins,  at  eight  cents  I 
a  |>ound  ? 

LESSON    VI. 

1.  Helen's  dress  contains  seven  yards  of  calico, 
which  cost  one  shilling  a  yard  :  what  was  the  cost 
of  her  dress  ? 

2.  At  three  cents  a  skein,  what  will  seven  skeins 
of  sewing  silk  cost  ? 

j      3.  At  two  cents  a  stick,  what  will  seven  sticks  of 
twist  cost  ? 

4.  The  fare  by  Railroad  from  Boston  to  Albany 
is  six  dollars  for  one  person:  what  wiil  it  be  for  a 
family  of  seven  persons  ? 

5.  Four  farthings  make  one  penny  :  how  many 
farthings  are  there  in  seven  pence  ? 

6.  If  a  stage  runs  five  miles  in  one  hour,  how  far 
will  it  run  in  seven  hours  ? 

7.  Harriet  had  seven  rose  bushes,  and  one  morn- 
ing  she  found  eight  roses  upon  each  :  how  many 
were  ticre  upon  all  ? 

8.  What  cost  seven  pounds  of  lard,  at  seven  cents 
a  pound  1 

9.  What  .cost  seven  dozen  chairs,  at  nme  dollars 
per  tiozen  i 

10.  At  ten  shillings  a  >ard,  what  is  the  cost  of 
seven  yai  Is  of  cloth  ? 


I 


MULTIPLICATION.  47 


LESSON    VII. 

1 .  What  will  eight  bushels  of  peaches  co&t,  at  one 
dollar  a  bushel  ? 

2.  If  a  quart  of  milk  costs  four  cents,  what  will 
be  t'le  cost  of  eight  quarts  ? 

8.  If  you  recite  three  perfect  lessons  a  day,  how 
many  will  you  recite  in  eight  days  ? 

4.  At  two  shillings  a  gallon,  what  will  eight  gal- 
lons of  molasses  come  to  ? 

5.  In  New  Kngland,  six  shillings  make  a  dollar  : 
how  many  shillings  are  there  in  eight  dollars? 

6.  At  five  cents  a  pound,  what  cost  eight  pounds 
of  figs  ? 

7.  There  are  eight  rows  of  trees  in  an  orchard, 
and  seven  trees  in  a  row  :  how  many  trees  are  there 

j  in  the  orchard  ? 

I      8.   In  New  York,  eight  shillings  make  a  dollar : 

[  how  many  shillings  are  there   in  eight  New  York 

I  dollars  ? 

I      9.  A  farmer  sold  eight  tons  of  hay,  at  nine  dol- 

;  lars  per  ton  :  how  much  did  he  receive  for  his  hay  ? 

i      10.   What  is  the  value  of  eight  cows,  at  ten  dollars 

i  apiece  ? 

;  LESSON    VI 11. 

i 

1.   In  one  quart  there  are  two  pints  :  liow  many 

'■  pints  are  th<^re  in  nine  quarts? 
!      2.    What  cosi  nine  caps,  at  one  dollar  apie/ce  ? 
■      3.  Thr'i.e  feet  make  a  yard  :  how  many  feet  are 
therp  m  nine  yards  ? 
I      4.   A  traveler  n^t  nine  beggars  and  gave  each  of 
j  them  four  shillings  :  how  many  shill-ngs  did  he  give 
I  to  all  ? 


48  MULTIPLICATION. 


5.  If  a  hunter  kills  five  pigeons  at  every  shot,  and 
fires  nine  times,   low  many  will  he  kill  ? 

6.  How  much  will  nine  quarts  of  blue-berries  : 
cost,  at  eight  cents  a  quart  ? 

7.  Henry's  mother  gave  him  six  cents  apiece  for: 
carrying  nine  billets  :  how  many  cents  did  he  receive 
for  all  ? 

8.  Susan  received  sev^n  shillings  a  week  fordoing 
the  work  of  the  family :  how  much  did  she  earn  in 
nine  weeks  ? 

9.  If  a  family  consumes  ten  pounds  of  butter  in 
a  week,  how  many  pounds  will  last  them  nine 
weeks  '( 

10.  What  fosi  nuie  cords  of  wood,  at  nine  shillings 
a  cord  ? 

LESSON   IX. 

1.  How  mu(,h  will  ten  sheep  cost,  at  two  dollars 
a  head  ? 

2.  How  much  will  ten  barrels  of  flour  cost,  at  five 
dollars  a  barrel  ? 

3.  At  four  dollars  a  yard,  what  will  ten  yards  of 
cloth  cost  ? 

4.  VVhat  cost  ten  bushels  of  corn,  at  three  shil- 
lings a  bushel  ? 

5.  What  cost  ten  coats,  at  eight  dollars  apiece  ? 

6.  A  farmer  gave  three  bushels  of  wheat  foi  a 
yard  of  cloth :  how  many  bushels  must  he  give  for 
ten  yards  ? 

7.  A  dairy- woman  bought  ten  yards  of  silk  and 
paid  for  it  in  butter,  giving  seven  pounds  for  ayc^d  : 
how  many  pounds  of  butter  did  her  silk  cost  ? 

8.  At  six  dollars  a  yard,  how  much  will  ten  yards  \ 
of  clcth  cost  ?  i 


MULTIPLICATION.  49 


9.  Ten  dollars  make  an  eagle :  how  many  dollars 
are  there  in  ten  eagles  ? 

10.  My  neighbor's  peach-orchard  contains  ten  rows 
of  trees,  and  there  are  nine  trees  in  a  row  :  how 
many  peach-trees  has  he? 

LESSON    X.* 

1.  How  many  times  two  make  eight?  How  many 
times  two  make  twelve?  Ten?  Fourteen?  Eigh- 
teen? Sixteen?  Twenty? 

2.  How  many  times  three  make  twelve?  Nine? 
Fifteen?  Twenty-one?  Eighteen?  Twenty-four? 
Thirty?    Twenty-seven? 

3.  Hpw  many  times  four  make  twenty?  Sixteen? 
Twelve?  Eight?  Twenty-four?  Thirty-two?  Thirty- 
six?  Forty? 

4.  How  many  times  five  make  twenty  ?  Thirty  ? 
Twenty -five?  Thirty -five  ?  Forty?  Forty-five? 
Fifty? 

5.  How  many  times  six  make  eighteen  ?  Thirty  ? 
Twenty-four?  Forty-two?  Thirty-six?  Sixty?  For- 
ty-eight? Fifty-four? 

6.  How  many  times  seven  make  twenty-eight? 
Thirty-five?  Twenty-one?  Forty-two?  Seventy? 
Sixty-three?  Fifty-six? 

7.  How  many  times  eight  make  twenty-four? 
Thirty-two  ?  Forty-eight  ?  Seventy -two  ?  Forty  ? 
Fifty-six?  Eighty?  Sixty-four? 

8.  How  many  times  nine  make  twenty-sevtn  ? 
Forty-five?  Thirty-six?  Fifty-four?  Seventy-two? 
Sixty-three?   Eighty -one?  Ninety? 


*  This  and  the  following  lesson  should  be  studied,  till  the  class 
can  answer  the  questions  with  great  promptitude.  This  they 
will  soon  be  al.le  to  do,  if  they  have  thoroughly  learned  the  Mul- 
tiplication Table, 


50  MULTIPLICATION. 


9.  3ow  many  timea  ten  make  thirty  ?  Twenty? 
Forty?  Sixty?  Fifty?  Ninety?  Eighty?  Seventy? 
One  hundred? 

LESSON  XI  . 

1.  Eight*  is  how  many  times  two?  Hew  many 
times  four  ?  How  many  times  one  ? 

2.  Twelve  is  how  many  times  two?  How  many 
times  three?  How  many  times  four?  How  many 
times  six  ?  How  many  times  one? 

3.  Eighteen  is  how  many  times  two?  How'^many 
times  six  ?  How  many  times  three  ?  How  many 
times  nine  ? 

4.  Sixteen  is  how  many  times  eight?  How  many 
times  four  ?  F\ow  many  times  two  ? 

5.  Twenty  ;s  how  many  times  two  ?  How  many 
times  five  ?  How  many  times  ten  ?  How  many  times 
four  ? 

6.  Thirty  is  how  many  times  five?  How  many 
times  ten  ?  How  many  times  six  ?  How  many  times 
three  ? 

7.  Twenty-four  is  how  many  times  four?  How 
many  times  three  ?  How  manv  times  six  ?  How 
many  times  eight  ?  How  many  tinir*  twelve  ?  How 
many  times  two  ? 

8.  Thirty-two  is  how  many  tim&s  eight?  How 
many  times  four? 

9.  Thirty-six  is  how  many  times  six?  How  many 
times  four?  How  many  times  three?  How  many 
times  twelve  ?     How  many  times  nine  ? 

10.  Twenty-seven  is  how  many  times  hree  ?  Hew 
many  time?  nine  ? 

*  The  number  eight,  &.c.,  is  M)nsidered  a  collective  noun,  con- 
veying the  idea  of  unity,  and  »h>refore  requires  a  verb  in  the 
singular  numb*r. 


MULTIPLICATION.  51 


1 1 .  Forty -two  is  how  many  times  six  ?  How  many 
times  se\en  ? 

12.  Fifty-six  is  how  many  times  seven?  How 
many  times  eight  ? 

13.  Thirty-five  is  how  many  times  seven?  How 
many  times  five  ? 

14.  Seventy -two  is  how  many  times  nine  ?  How 
many  times  eight  ? 

LESSON  XII. 

1.  What  cost  five  oranges,  at  three  cents  apiece  ? 

2.  What  cost  six  tfiimbles,  at  four  cents  apiece  ? 

3.  A  teacher  bought  ten  inkstands,  at  six  cents 
apiece  :  what  did  they  come  to  ? 

4.  If  four  boys  sit  on  one  bench,  how  many  can 
sit  on  five  benches  ?  On  seven  benches  ? 

5.  Jane  bought  five  yards  of  silk  braid,  at  four 
cents  a  yard  :  how  much  did  it  come  to  ? 

6.  Horace  bought  four  young  rabbits  for  eight 
shillings,  and  sold  them  for  three  shillings  apiece  : 
did  he  gain  or  lose  by  his  bargain  ?   How  much  ? 

7.  VVhat  will  ten  pounds  of  figs  cost,  at  eight 
cents  a  pound  ?  At  nine  cents  ? 

8.  When  beef  is  six  dollars  a  hundred,  what 
will  a  fatted  ox  co»ne  to  which  weighs  nine  hundred 
pounds  ? 

9.  If  one  stage  can  carry  nme  pasvsengers,  now 
miny  can  four  stages  carry  ? 

10.  What  cost  nine  pounds  of  tea,  at  six  shillings 
a  pound  ' 

11.  if  five  yards  of  cloth  will  make  one  cloak, 
Kjw  many  yards  wili  six  olouiws  re^-.'i'^  "^ 

12.  If  a  horse  travels  six  miles  an  hour,  how  far 
will  he  travel  in  ten  hours  ? 


62  MULTIPUCATION. 


LESSON   XIII. 

1.  Q'  What  is  the  operation  called,  by  which  the 
preceding  examples  in  this  section  have  been  solved  ? 

Ans,  It  is  called  Multiplication. 

2.  Q.  What  is  Multiplication  ? 

Ans.  Multiplication  is  the  process  of  finding  the 
avnount  of  a  given  number  repeated  or  added  to  itself, 
a  given  number  of  times. 

3.  Q.  What  16  the  number  to  be  repeated,  or  mul- 
tiplied, called  ? 

Ans.  The  Multiplicand. 

4.  Q.  What  is  the  number  by  which  we  multiply, 
called  f 

Ans.  The  Multiplier. 

5.  Q.  What  is  the  answer,  or  number  produced  by 
multiplication,  called ! 

Ans.  The  Product. 

6.  Q.  What  is  meant  by  the  term  product  ? 
Ans.  Something  that  is  jyrodu4;ed  or  formed. 

Y.  When  we  say,  three  times  six  are  eighteen ; 
which  is  the  number  to  be  multiplied  ?  Which  is  the 
number  to  multiply  by?     Which  the  product? 

8.  When  we  say,  four  times  five  are  twenty; 
which  is  the  answer?  What  is  the  four  called? 
What  is  the  five  called  ?  What  is  the  iweyity 
called  ? 

9.  What  is  the  product  of  seven  multiplied  hy 
six  ? 

10.  What  is  the  product  of  nine  multiplied  bv 
five? 

11.  What  is  the  product  of  eight  multiplied  by 


SIX 


I  MULTIPLICATION. 


I  12.  What  is  the  product  of  seven  times  nine  1  Of 
I  eight  .imes  eight  ?  Of  seven  times  six  ? 
1  13  What  is  the  product  of  eight  times  seven  ?  Of 
j  nine  times  eight  ?  Of  nine  times  seven  ?  Of  six 
times  nine  ?  Of  seven  times  five  ?  Of  nine  tinnes 
I  five  ?  Of  seven  times  ten  ? 

14.  Which  is  the  most,  three  times  four,  or  four 
times  three  ? 

Note. — To  iUiistrate  ttiis  point,  move  out  four  balls  on  the  lower 
wire,  and  four  apiece  on  the  seroinl  and  third  wires.  This  will 
denote  three  times  four,  or  four  added  to  itself  three  times,  which 
the  pupil  will  perceive  make  twelve. 

Again,  letting  these  remain  in  their  present  place,  move  out 
three  balls  on  the  upper  wire,  also  three  apie<e  un  the  next  three 
wires.  This  will  denote  four  times  three,  or  three  added  to  it- 
self four  times,  whicli  the  pupil  will  see  make  twelve,  and  is 
therefore  the  same  a.s  three  times  four. 

15.  Which  is  the  most,  five  times  three,  or  three 
times  five  ? 

16.  Which  is  the  most,  five  times  six,  or  six  times 
five  ?  Six  times  seven,  or  seven  titnes  six  ? 

EXAMPLES    FOR    PRACTICE. 

1.  What  will  six  pair  of  skates  cost,  at  five  shil- 

]  lings  a  pair  ?  , 

2.  What   will    four  caps  cost,  at  eight  shillings  j 
apiece  ?  i 

3.  How  much  will  nine  quarts  o^  t'  erries  come 
to,  at  seven  cents  a  quart  ? 

4.  A  ten  dollars  apiece,  how  much  yfiW  three 
ploughs  cost  ?  I 

5.  A    farmer  sold  nine  lambs,  at  eight  shillings  I 
apiece  :  how  much  did  they  come  to  1  I 

6.  If  a  man  gives  six  bushels  of  oats  foi  one  pair  | 


54  MULTIPf  ICATION. 


of  boots,  how  many  bushels  must  be  give  ibr  seven 
pair  of  boots  ? 

7.  If  six  men  do  a  piece  of  work  in  ten  days,  how 
long  V*  ill  it  take  one  man  to  do  it  ? 

8.  At  seven  cents  a  bunch,  how  much  will  eight 
bunches  of  radishes  cost  ?    Nine    bunches  ?     Ten  ' 
bunches  ?  I 

9.  VV^hich  is  the  most,  eight  times  seven,  or  nine  ; 
times  six  ?  Six  times  six,  or  four  times  nine  ?  Eight 
times  eight,  or  seven  times  nine  ? 

10.  A  farmer  bought  six  pair  of  shoes,  at  two  dol- 
lars a  pair,  and  paid  four  cords  of  wood  worth  two 
dollars  a  cord  :  how  much  did  he  still  owe  for  his 
shoes  ? 

1 1 .  Twenty-eight  is  how  many  times  seven  ?  How 
many  times  four  ?  Sixty-three  is  how  many  times 
nine  ?  Forty-eight  is  how  many  times  six  ? 

12.  Fifty-six  is  how  many  times  eight?  Forty-five 
is  how  many  times  nine  ?  Forty-two  is  how  manv 
times  six  ?  Forty-nine  is  how  many  times  seven  ? 

18.  Kighty-one  is  how  many  times  nine  ?  Forty  is 
how  many  times  ten  ?  Eigiity  is  how  many  times 
ten  ? 

14.  VV^hich  is  trlie  most,  four  times  eight,  or  three 
times  nine  ? 

15.  Which  is  the  most,  five  times  seven,  or  four 
times  ten  ? 

16.  Which  is  the  most,  six  times  eii^nt,  or  nine 
times  six  ? 

17.  Which  is  the  most,  seven  times  nine,  or  eight 
..  *imes  seven  ? 

{       18.  If  side  Combs  cost  nine  cents  a  pair,  what  will 
five   pair  cost?     Eight   pair?    Nine  pair?     Seven 
!  pair  ?  Ten  pair  ? 


MULTIPLICATION.  55 


19.  VVhat  cost  nine  papers  ot*  pins,  at  two  shillings 
a  paper  ?  At  four  shillings  ? 

20.  Nine  times  three  are  how  many  ?  Nine  timet< 
focir  ?  Nine  times  six  ? 

21.  If  a  barrel  of  maple  sap  will  make  eight 
pounds  of  sugar,  how  many  pounds  will  four  barrels 
mako  ?  Seven  barrels  ?   Right  barrels  ? 

2'2.  What  cost  seven  penknives,  at  six  shillings 
apiece  ? 

23.  Kdwin  bought  six  pencils  and  gave  two  apples 
apiece  for  them  ;  also  four  quills  and  gave  three  ap- 
ples apiece  for  them  :  how  many  apples  did  he  give 
for  his  pencils  and  (juills  together? 

24.  If  one  acre  of  ground  produces  ten  bushels  of 
wheat,  how  many  bushels  will  six  acres  produce  ? 
Ten  acres  ? 

2.5.  Seven  times  six  are  how  many  ?  Seven  times 
eight  ?  Seven  times  nine  ?  Eight  times  nine  ''  Six 
times  nine  ? 

26.  Charlotte  bought  six  primers,  at  nine  cents 
apiece  :  what  did  they  come  to  ? 

27.  A  lady  bought  ten  yards  of  calico,  at  ten  cents 
a  yard  ;  and  four  spools  of  cotton,  at  five  cents  a 
spool  :  what  did  her  bill  amount  to  ? 

25.  A  man  bought  ten  sheep,  at  two  dollars  a 
head  ;  and  four  cows,  at  ten  dollars  a  head  :  how 
much  did  he  give  for  all  ? 

29.  Henry  bought  seven  quarts  of  cheiiies,  a* 
nine  cents  a  quart ;  and  ten  quarts  of  strawberries, 
at  six  cents  a  quart :  which  cost  the  most  ? 

30.  VVhich  will  cost  the  most,  nine  slates  at  eight 
centn  apiece^  or  ten  inkstand*  at  seven  cents  apiece  ? 


SECTION  V. 

DIVISION. 

LESSON    I. 

1.  How  mau}  pears,  at  two  cents  apiece,  can  you 
buy  for  six  cents  $ 

Analysis. — Since  two  cents  will  buy  one  pear,  six 
cents  will  buy  as  many  pears,  as  two  cents  are  con- 
tained times  in  six  cents ;  and  two  cents  are  contained 
in  six  cents,  three  times.  Therefore  six  cents  will  buy 
three  pears,  at  two  cents  apiece. 

2.  At  two  cents  a  yard,  how  many  yards  of  tape 
can  you  buy  for  four  cents  ? 

Suggestion. — To  find  how  many  times  two  cents 
are  contained  in  four  cents,  the  learner  must  think 
how  many  times  two  make /owr. 

3.  At  two  cents  apiece,  how  many  oranges  can  be 
bought  for  six  cents  ? 

4.  George  bought  ten  marbles,  which  he  divided 
among  his  little  brothei-s,  giving  them  two  a}>iece  : 
how  many  brothers  had  he  ? 

Suggestion. — Since  he  gave  two  maibles  to  each, 
he  manifestly  had  as  many  brothers,  as  two  marbles  \  * 
are  contained  times  in  ten  marbles. 

Note.—'^\\Q  principle  of  dividing  may  be  illustrated  in  the  fol- 
lowinsr  manner  :  Pass  acrosR  ten  balls  on  one  of  the  wires,  which 
may  represent  the  ten  marbles.  Now  since  he  gave  two  marbles 
to  each  brother,  moving:  out  two  balls  will  denote  one  brother; 
movinor  out  two  more  will  denote  another  share,  and  so  on,  every 
two  I  alls  will  denote  one  brother,  till  all  the  balls  are  removed  or 
exliai  ?ted.  Finally,  counting  the  number  of  twos  or  pair  of  l5;dls 
moved  out,  it  will  sliow  how  many  times  two  marbles  are  con- 
tained in  ten  marbles,  which  is  the  number  of  brothers  he  had. 


DIVISION. 


57 


5.  How  many  load  pencils,  at  two  cents  apiece, 
can  you  buy  for  eiglit  cents  ? 

6.  Henry  had  twelve  shillings  which  he  laid  out 
in  books,  at  two  shillings  aj)iece  :  how  many  books 
did  he  buy  ? 

7.  Julius  had  fourteen  marbles  which  he  wished 
to  divide  into  two  equal  piles  :  how  many  must  he 
pat  in  a  pile  ? 

8.  How  many  pounds  of  ginger,  at  two  shillings 
a  pound,  can  be  bought  for  sixteen  shillings  ? 

9.  A  tnan  laid  out  eigliteen  shillings  in  apples,  at 
two  shillings  a  bushel  :  how  many  bushels  did  he 
buy  ? 

10.  A  man  bought  twenty  dollars  worth  of  shoes, 
at  two  dollars  a  pair  :  how  many  pair  did  he  buy  ?* 

Note. — The  Divismn  Table  should  be  studied  in  the  same  man- 
ner as  the  preceding  Tables. 

DIVISION     TABLE. 


Two  ui  two, 

Two  "  four, 

Two  "  Bix, 

Two  •'  eight, 

Two  "  ten, 


once. 

two    limf* 

three  " 
four  " 
five      " 


Two  in  twelve, 

Two  "  fourteen. 

Two  "  sixteen, 

Two  "  eighteen, 

Two  "  twenty. 


SIX     tiniM 

seven  ** 
eight  " 
nine  " 
ten      " 


!  Three 

ill  three, 

once. 

Three 

ineiguteen,       six    time.. 

Three 

"six, 

two    time.. 

Three 

"  twenty-one,  seven  " 

Three 

"  nine. 

three  " 

Three 

"  twenty-four,  eight  •' 

i  Three 

"  twelve, 

four     " 

Three 

*  twenty-sev,,  nine   "      | 

1  Throe 

"  tilleon, 

five      " 

Three 

"  thirty,             ten      " 

Four 

iK  four, 

once. 

Fo'ir 

in  twenty- four,  six   ti»e.. 

Four 

"  eight, 

two    tmiei. 

Foot 

"  twenty-eigh)  seven  ** 

Pour 

"  twelve, 

three    " 

Four 

"thirty-two,     eight  " 

Four 

"  sixteen. 

four     " 

Four 

"  thirty-six,       nine   " 

Pour 

'« twenty, 

five       " 

Four 

"  forty,                .n      " 

58 

DIVISION. 

Five    tofivs, 

once. 

F'ive    in  thirty, 

six      tiaM. 

Five 

'ten, 

two   timet 

Five 

'  thirty -five, 

seven  " 

!  Five    ' 

'  fifteen, 

three  " 

Five 

'  forty, 

eight   " 

Five 

'  twenty, 

four    " 

Five 

'  forty-five, 

nine    "      j 

Five 

'  twen.y-five, 

five     " 

Five 

'fifty. 

ten      "      I 

Six     . 

nsix. 

once. 

Six     in  thirty-six, 

six    ttoM. 

:  Six 

'  twelve, 

two    Ume. 

Six 

'  forty-two. 

seven  " 

j  Six 

'  eighteen, 

three   " 

Si<x 

'  forty-eight. 

eight  «      1 

Six 

'  twenty-four, 

four     " 

Six 

'  fifty-four. 

nine    " 

Six 

'  thirty, 

five      " 

Six 

♦  sixty, 

ten      " 

Seven 

in  seven, 

once. 

Seven 

11.  forty-two, 

six        tlBBM. 

Seven 

'  fourteen, 

two    timei. 

Seven 

'  forty- nine. 

seven  " 

Seven 

'  twenty-one. 

three  " 

Seven 

'fifty -six, 

eight  " 

Seven 

"  twenty-eight,  four     " 

Seven 

'  sixty-three. 

nine    " 

Seven 

'  thirty-five, 

five     " 

Seven 

' seventy. 

ten      " 

Eight 

1.  eight. 

once. 

Eight 

n  forty-eight, 

six        tUDM. 

1  Kight 

'  sixteen. 

two    times. 

Eight 

'  fifty-six. 

seven  " 

Eight 

'  twenty- four, 

three   " 

Eight 

'  sixty-four. 

eight   " 

1  Right 

'  thirty-two, 

four     " 

Eight 

'  seventy-two 

nine    " 

'  Eight 

'  forty, 

five      " 

Ei^ht 

"  eighty. 

ten       " 

INine 

n  nine, 

once.    • 

Nine 

n  fifty-fitur, 

six      tin.e». 

iNinc 

"  eighteen, 

two    limea. 

Nine 

"  sixty-three. 

seven  " 

j  Nine 

■'twenty-sev., 

three  " 

Nine 

''  seventy-two 

,  eight  " 

iNine 

"thirty-six, 

four     " 

Nine 

"  eighty-one, 

nine    «      i 

Nine 

"  forty-five 

five      " 

Nine 

"  ninety, 

ten      « 

Ten 

111  ten. 

once. 

jTen 

uisixtv, 

six     timet      j 

Ten 

"  twenty. 

two    timaa. 

Ten 

"  seventy, 

seven  "      I 

Ten 

"  thirty, 

three   " 

Ten 

"eighty, 

eight  "       1 

Ten 

"forty, 

four     " 

Ten 

■•'  ninety 

nine    "      j 

Ten 

"fifty, 

five      ' 

Ten 

"a  hundred, w 

ten      "      1 

1 
1 

DIVISION.  59 


•& 


I  LESSON   II 

\  1.  When  oranges  are  three  cents  apiecej  how  I 
many  can  you  buy  for  six  cents  ?  How  many  times  i 
three  make  six  ?  I 

2.  At  three  cents  a  yard,  how  many  yards  of  rib- 
bon can  you  buy  for  nine  cents  ?     How  many  times  i 
three  make  nine  ?  | 

3.  George  has  twelve  apples  which  he  wishes  to  i 
'  divide  equally  among  three  of  his  companions :  how  1 
j  many  will  each  receive  ?     How  many  times  three  \ 

make  twelve  ?  i 

I      4.  A  man  divided  eighteen  oranges  equally  amon 
his  three  sons  :  how  many  did  each  receive  ? 

5.  If  you  walk  three  miles  an  hour,  how  long  j 
will  it  take  you  to  walk  fifteen  miles  ?  How  many  ! 
times  three  make  fifteen  ?  | 

6.  If  you   had  twenty-one  marbles  to  give  three  \ 
of  your  companions,  how  many  could  you  give  them 
apiece  ? 

7.  How  many  barrels  of  cider,  at  three  dollars  a 
barrel,  can  I  buy  for  twenty-four  dollars?  How 
many  times  three  in  twenty-four  ? 

8.  A  man  wishes  to  set  out  twenty-seven  peach- 
irees  in  three  rows :    how  many  must  he  put  in  a 

,  row  ? 

'      9.  Three  boys  caught  thirty  fishes,  and  agreed 
i  to  divide  them  equally :  how  many  will  each  one  j 
I  have  ? 

10.  If  one  man  can  do  a  piece  of  work  in  twen- 
I  ty-one  days,  how  long  will  it  take  three  men  to 
I  do  it  ? 


60  DIVISION. 


LESSON   III. 

1.  How  many  lemons,  at  four  cents  apiece,  can 
be  bought  for  eight  cents  ?  How  many  times  four 
make  eight  ? 

2.  At  four  shillings  a  gallon,  how  many  gallons 
of  molasses  can  be  bought  for  twelve  shillings? 

3.  William  desires  to  divide  twenty  apples  equal- 
ly among  four  boys :  how  many  must  he  give  them 

i  apiece  ? 

4.  Four  scholars  recited  twenty-four  questions  in 
arithmetic :  how  many  questions  did  each  recite  ? 

5.  The  price  of  a  pair  of  boots  is  four  dollars : 
how  many  pair  can  I  buy  for  sixteen  dollars? 

6.  If  a  man  walks  four  miles  an  hour,  how  long 
will  it  take  him  to  walk  thiily-two  miles  ? 

7.  How  long  will  it  takf>  him  to  walk  twenty- 
eight  miles,  at  four  miles  an  hour? 

is.  Four  boys  find  a  piirse  containing  thirty-six 
cents,  which  they  wish  to  divide  equally  :  how  many 
cents  will  each  one  receive  ? 

9.  A  school  which  contained  forty  scholars,  was 
divided  into  four  equal  classes :  how  many  scholars 
were  there  in  a  class  ? 

LESSON    IV. 

1.  How  many  spools  of  cotton  at  five  cents  a 
•^pool,  can  be  bought  for  ten  cents  ?  How  many 
times  five  nmke  ten  ? 

2.  How  ujany  barrels  of  flour,  at  five  dulars  a 
barrel,  can  you  buy  for  twenty  dollars? 

8.  At  five  shillings  a  pound,  how  many  pounds 
of  tea  can  I  buy  for  fifteen  shillings  ? 


DIVISION.  61  j 


4.  At  five  cents  a  pound,  how  many  pouncUi  of 
lard  can  be  bought  for  thirty  cents  ? 

5.  James  has  twenty-five  cents  which  he  wishes 
to  lay  out  in  lemons,  which  cost  five  cents  apiece  * 
how  many  can  he  buy  ? 

6    When  milk  is  five  cep*s  a  quart,  how  many  ; 
quaits  can  you  buy  for  fort}   cents ? 

7.  If  you  have  fifty  cenU    how  many  tops  can  you  , 
buy,  at  five  cents  apioce  ?  I 

8.  If  a  man  travels  fiv*  miles  an  ho«r,  how  long  j 
will  it  take  him  to  travel  forty-five  miles? 

9.  How  lotijir  will  it  take  a  man    to  travel  fifty 
I  miles,  if  he  travels  five  miles  an  hour? 

j  LESSON    V. 

I       1.   If  I   had  twelve  cents,  how  many  bunches  of 
i  quills  could  I  buy,  at  six  cents  a  bunch  ? 
I      'Z,   If  you  had  twenty-four  peaches  to  give  to  six  ! 
.  of  your  companions,  how  many  could  you  give  them  i 
j  apiece  ?  i 

I      3.  At  six  dollars  a  yard,  how  many  yards  of  cloth  ' 
j  can  I  buy  for  eighteen  dollars?  j 

j      4.  At  six  cents  an  ounce,  how  many  ounces  of  i 
!  peppermints  can  you  buy  for  thirty  cents?  j 

j      5.   How   many   hats,   at  six   dollars  apiece,  will  I 
forty-two  dollars  buy  ? 

6.  How   many   pounds  of  tea,  at  six  shillings  a 
!  pound,  will  thirty-six  shillings  buy? 

7.  A  man  laid  out  sixty  shillings  for  lambs,  at  gix 
shillings  apiece  :   how  many  did  he  buy  ? 

8.  A  merchant  paid  fifty-four  dollars  for  six  mufTs 
i  how  much  was  that  apiece  ? 

'      9.  At  six  shillings  a  bu«hel,  how  many  bushels  of 
j  wheal  will  forty-eight  shillings  buy  ? 


.»2  DIVISION. 


LESSON    VI. 

1.  Sarah  bought  seven  yards  of  silk  braid  for 
twenty-eight  cents :  how  much  did  she  give  a  yard  ? 

2.  Susan  laid  out  forty-two  cents  for  ribbon  worth 
seven  cents  a  yard  :  how  many  yards  did  she  get  ? 

3.  If  seven  yards  of  cloth  make  one  suit  of  clothes, 
how  many  suits  will  twenty-one  yards  make  ? 

4.  A  teacher  wishes  to  give  fourteen  pencils  to  a 
class  of  seven  scholars :  how  many  pencils  can  he 
give  to  each  ? 

5.  George  has  thirty-five  pears  to  give  to  seven 
boys :  how  many  can  he  give  them  apiece  ? 

6.  At  seven  cents  a  pound,  how  many  pounds  of 
cotton  can  be  bought  for  fifty-six  cents  ? 

7.  Seven  days  make  a  week :  how  many  weeks 
are  there  in  forty-nine  days  ? 

8.  If  a  stage  goes  seven  miles  an  hour,  how  long 
will  it  be  in  going  seventy  miles  ? 

9.  A  man  paid  sixty-three  cents  for  seven  pounds 
of  sugar,  wliat  was  that  a  pound  ? 

LESSON   VII. 

1.  A  man  gave  sixteen  shiliings  to  eight  oeg- 
gars :  how  much  did  he  give  to  each  ? 

2.  Sarah  has  twenty-four  roses  to  give  to  eight 
little  girls:  how  many  can  she  give  them  apiece? 

3.  How  many  sheep,  at  eight  shillings  a  head,  can 
I  buy  for  forty  shillings  ? 

4.  Eight  quarts  make  a  peck :  how  many  pecks 
are  there  in  thirty-two  quarts  ? 

5.  At  eight  dollars  a  ton,  how  much  coal  can  I 
buy  for  sixty.four  dollars? 


DIVISION.  63 


6.  When  cherries  are  eight  cents  a  quart,  hoM' 
many  quarts  can  you  buy  for  fifty  six  cents  ? 

7.  If  you  have  forty-eight  cents,  how  many  slates 
can  you  buy,  at  eight  cents  apiece  ? 

8.  If  you  read  eight  pages  a  day,  how  long  will 
it  taiie  you  to  read  a  book  through,  which  has  sev- 
enty-two pages  ? 

9.  If  a  school  contains  eighty  scholars,  how  many 
classes  can  be  formed  containing  eight  scholars 
apiece  ^ 

LESSON    Vlll. 

1.  When  butter  is  nine  cents  a  pound,  how  many 
pounds,  will  twenty-seven  cents  buy  ? 

2.  At  nine  dollars  a  barrel,  how  many  barrels  of 
beef  can  I  buy  for  thirty-six  dollars? 

8.  If  nitie  yards  of  cloth  will  make  one  cloak, 
how  many  cloaks  will  eighteen  yards  make  ? 

4.  If  yoii  can  buy  a  quart  of  molasses  for  nine 
cents,  how  man)  {uarts  can  you  b'l.y  for  forty-five 
cents  1 

5.  If  nine  yards  of  silk  cost  seventy-two  shillings, 
what  will  one  yard  cost? 

6.  A  man  paid  sixty-three  dollars  for  nine  tons 
of  hay  :  what  was  that  per  ton  ? 

j      7.  A  tavern-keeper  gave  fifty-four  quarts  of  oats 

'  to   nine   horses :  how   many   quarts  did  he  give  to 

I  each  horse  ? 

I      8.  If  you  recite  nine  questions  in  arithmetic  a  day, 

i  how  many  days  will  it  take  you  to  recite  eighty -one 

,  questions? 

j      9.   How  many  cows,  at  nine  dollars  apiece,  can  a 

I  man  buy  for  ninety  dollars  ? 


J 


64  DIVISION. 


LESSON    IX. 

1.  How  many  cows,  at  ten  dollars  a  head,  can  a 
man  buy  for  twenty  dollars "? 

2.  A  certain  school  contained  forty  scholars,  which 
the  teacher  formed  into  classes  of  ten  scholars  each  : ! 
how  many  classes  did  he  form  ? 

3.  At  ten  dollars  per  acre,  how  many  acres  of 
land  can  be  bought  for  nfty  dollars? 

4.  A  man  paid  eighty  cents  for  a  horse  and  chaise 
to  ride  ten  miles :  how  much  was  that  a  mile  ? 

5.  How  many  sheep,  at  ten  shillings  a  head,  can 
be  bought  for  ninety  shillings  ? 

6.  A  man  laid  out  sixty  dollars  for  hay,  at  ten 
dollars  per  ton  :  how  many  tons  did  he  buy  ? 

7.  If  I  pay  ten  cents  a  quart  for  blackberries, 
how  many  quarts  can  I  buy  for  thirty  cents  ? 

8.  A  dairy- woman  has  seventy  pounds  of  butter, 
which  she  wishes  to  divide  equally  among  ten  cus- 
tomers :  how  many  pounds  can  she  send  to  each  ? 

9.  If  you  divide  a  hundred  marbles  into  ten  equal 
piles,  how  many  will  there  be  in  a  pile  ? 

LESSON    X 

I       1.  In  eight,  how  many  times  four?     How  many 
times  two  ?     How  many  times  one  ? 

2.  In  six,  how  many  times  two  **  How  many 
times  three  ?    One  ?    Six  ? 

3.  In  twelve,  how  many  times  two?  Three? 
Four  ?     Six  ? 

4.  In  ten,  how  many  times  five  ?     Two  ?     One  ? 

5.  In  sixteen,  how  many  times  eight?  Four? 
Two?    One? 


1 

1 

1 

DIVISION. 

1 
65, 

1 

1 

'       6. 

In  twenty. 

four,  how  many 

times  two  ? 

Three  ? 

Four 

?    Six?     P 

:ight  ? 

-r 

In  eighteen,  how  maii}' 

limes 

two? 

Three  ? 

Sx? 

Nine  ? 

i 

8. 

In  twenty, 

how  many  times  two 

?  Ten 

?  Five? 

9. 

In   thirty-six,  how   nnany 

times  six  ? 

Nine  ?  | 

Three  ?    Four  ? 

Two? 

1 

i       ^<^ 

In  thirty- 

two,  how  many 

times  eijjht  ? 

Four  ? 

!     n 

Jn    l'.venty-ei<rht,    how    many 

times 

seven  ?  i 

Four  ?    Two  ? 

12.   In  forty,  how  many  tijufs  ten?  Fight  ?  Five  ? 
18.   In  forty-eitrht  how  many  times  eight?  Six  ? 

14.  In  sixty-three,  how  many  times  seven  ?  Nine  ? 

15.  In  fifty -six,  how  many  times  seven  ?    Eight  ? 

LESSON    XI  .  I 

1.  How  many  t''mos  is  three  contained  in  twelve  ?  j 
I  T  citrhleen  ?  In  fiJ^oon?  In  twontvone?  In  twenty-  i 
fc' ir  ?    In  thirty  ?    in  twenty-seven  ?  I 

J.  IIow  many  times  is  five  contained  in  fifteen  ?  ' 
In  twenty-five  ?     In  thirty  five?    In  fifty  ? 

8.   IIow  many  times  is  four  contained  in  sixteen  ? 
In  twenty. four  ?   In  thirty  two?    In  forty?    In  thirty-  i 
six?    In  twenty-eight  ?  .; 

4.  How  many  times  is  six  contained  in  eighteen  ?  ' 
In  thirty?  In  twenty-four?  In  thirty-six?  In  forty-  \ 
two  ?  ^  In  fifty- four  ?  ! 

5.  How  many  times  is  eight  contained  in  twenty  ' 
four?  In  thirty-two?  In  forty-eight  ?  In  sixty-four  ?  j 
Inffty-six?    In  seventy-two  ?  I 

6.  IIow  many  times  is  seven  contained  in  twenty-  ■ 
eight?     In  thirty-five  ?     In  forty-two?     In  fifty-six  ? 
In  fort} -pine  ?    In  sixty-three  ?  ! 


1^  ■ 

DIVISION.                                                     1 

j 

1 

1      7. 

[low  many  times  is  nine  contained  in  twenty. 

seven 

?    In  forty-five?    In  thirty-six?    In  fifty  four? 

In  sixtv-three  ?                                                                       | 

H. 

In  thirteen,  how  many  times   four,  aid   how 

many 

over  ?                                                                         1 

Ans.  Three  times,  and  one  over.                               |i 

9. 

Why  ?                                                                     1 

Am.  Because,  three  times  four  are  twelve,  acd  1 

twelve  from  thirteen  leaves  one.                                    || 

1« 

In  seventeen,  how  many  times  five,  and  how  1 

many  over  ?                                                                      !| 

11 

in  twenty.six,  how  many  times  six,  and  how  j 

1  many 

over  ?                                                                         } 

i-i. 

In  twenty,  how  many  times  three,  and  how  i 

many 

over  ? 

18 

In  forty-three,  how  many  times  five,  and  how 

many 

over  ? 

14. 

In  thirty-nine,  how  many  times  six,  and  how 

many 

over? 

1. 

LESSON    XII. 

How  many  oranges,  at  four  cents  apiece,  can 

you  h 

uy  /or  twenty  cents  ? 

2. 

How  many  thimbles  can  Sarah  buy  for  t:  irty- 

five  cents,  if  she  pays  seven  cents  apiece?                    | 

3. 

George  paid  twenty-four  cents  for  six  lead  pen- 

cils: 

how  much  was  that  apiece? 

!    4. 

A  man  gave  fcrty-five  dollars  for  nine  sheep: 

i  what 

was  the  price  of  the  sheep  per  head? 

5. 

It  a  man  travels  soven  miles  an  hour,  how  lonti 

vvjl.  ii  take  him  t)  travel  sixtv-three  miles?                 l| 

;       6. 

A  gentleman  divided  thirty-five  cents  equally 

1  amon 

g  five  boys  :  how  many  cents  did  each  receive  ?  j 

-.-. .- - J 

DIVISION.  67 


7.  How  many  barrels  of  flour,  at  six  dollars  a  bar- 
rel, can  be  boui^ht  for  forty -eight  dollars? 

8.  A  hatter  had  forty  hats,  which  he  packed  in  five 
boxes :  how  many  did  he  put  in  a  box  ? 

9.  A  man  wishes  to  walk  from  New  Haven  to  Hart- 
ford, a  distance  of  thirtv-six  miles  '.  how  long  will  it 
take  him,  if  he  walks  four  miles  an  hour  ? 

10.  Seven  boys  found  a  pocket-book  containing 
forty-nine  dollars,  which  they  shared  equally:  how 
much  did  each  receive? 

11.  When  c<:»al  is  eight  dollars  a  ton,  how  much 
can  I  buy  for  fifty -six  dollars? 

12.  If  one  man  can  b  li!  1  a  barn  in  forty  days,  how 
;  long  would  it  take  four  men  to  build  it  ? 

LESSON    XIII. 

1.  Q.  What  is  the  operation  called,  by  which  the 
preceding  examples  in  this  section  have  been  solved  ? 

I      Ana.  It  is  called  Divuion. 

2.  Q.  What  is  Division  ? 

Ans.  Division  is  tht  process  of  finding  how  many 
times  one  given  number  is  contained  in  another, 

3.  Q.  What  is  the  number  to  be  divided,  called  ? 
Ans.  The  Dividend.  _f'\ 

4.  Q.  What  is  the  number  by  which  we'  divide, 
called  ? 

Ans.  The  Divisor. 

5.  Q.  What  is  the  answer,  or  number  obtained  oy 
iivision,  called  ? 

A718.  The  Quotient.  I 

6.  Q.  What  ii^  the  number  that  is  sometimes  left 
after  dividing,  called  ? 

Ans.  The  Remainder. 


69  DIVISION. 


7.  When  we  say  four  is  contained  in  twenty- 
seven,  six  times  and  three  over,  wliich  is  the  num- 
ber to  be  divided  ?  Which  the  number  we  divide 
by?   Which  the  quotient  ?   Which  the  remaindei  ?      | 

H.  When  we  say,  five  is  contained  in  tiiirty-eight. 
seven  times  and  nree  over,  what  is  the  five  called 't 
What  is  the  thir  y-e'itrht  called  ?  What  is  the  seven 
sailed?   What  is  the  three  called? 

y.  What  is  the  quotient  of  twenty-three  divided 
by  tour,  and  what  the  remainder  ?  | 

10.  Five  in  twenty-eight,  how  many  times,  and 
what  the  remainder? 

11.  Six  in  thirty-four,  }k)w  many  times,  and  how 
many  over? 

\-z.  Eight  in  fifty,  how  many  times,  and  how  many 
over  ^ 


EXAMPLES    FOR    PRACTJCK. 

1.  itcorge  )>nid  twenty-four  cents  for  six  Jemons: 
how  muon  did  they  cost  apiece  ? 

2.  It  a  man  walks  five  miles  an  hour,  how  long 
will  it  taKc  him  to  go  forty  mihs? 

.3.  How  many  yards  of  ribbon,  at  seven  cents  a 
yard,  can  v^ou  purchase  for  twenty-one  cents?  For 
thirty-five  cents?    For  forty-two  cents? 

4.  How  many  thimbles,  at  six  cents  apiece,  can 
Mary  buy  tor  twenty-four  cents?  For  thirty  cents? 
For  forty-two  cents?     For  fifty- four  cents? 

^^.   At  eight  cents  a  quart,  how   many  quarts  of  j 
blackberries  can  you   buy  tor  sixteen  cents?     For 
thirty-two    cents?       For    forty-eight    cents?       For 
twenty-four  ceiils? 


^  DIVISION.  69 


6.  A  man  paid   forty  dollars   for  eight  yards  of  j 
cloth  :  hDW  much  was  that  per  yard  1 

7.  Henry  had  sixty-four  marbles,  which  he  ^ave 
to  eight  companions:   how  much  did  each  receive?    ' 

8.  In  three  times  four,  hv)w  many  times  two? 
So/utio7i.—r-Thri'.e  times  four  are  twelve  :  and  two 

is  contained  fii  twelve,  six  times,     ^ns.  Six  times. 

9.  In  two  tin»es  eight,  hew  many  limes  four  ? 

10.  In  three  times  six,  how  many  times  nine  ? 

11.  In  eight  times  three,  how  many  times  six  ? 

12.  In  four  times  ten,  how  many  times  eight?         i 

13.  In  five  times  four,  how  many  tin>es  ten  t  | 

14.  In  six  times  six,  how  many  times  nine  ?  j 

15.  Three  times  six  are  how  many  times  two? 

I       16.   Four  times  six  are  how  many  tinies  eight  ? 

17.  Six  times  six  are  how  many  times  four  ? 

18.  How  many  weeks  are  there  in  forty-two  days, 
there  being  seven  days  in  a  week?  In  thirty-five 
days,  how  many  weeks  ? 

19.  A  man  laid  out  twenty-eight  shillings  in  wheat. 
at  seven  shillings  a  bushel  :  how  many  bushels  did 
he  buy  ? 

20.  I  f  slates  cost  eight  cents  apiece,  how  many  can 
you  buy  for  sixty-four  cents  ? 

21.  If  the  price  of  coffee  is  nine  c^-^.ts  a  pound, 
how  many  pounds  can  I  buy  for  forty-five  cents? 
For  sixty-three  cents  ?   For  seventy-two  cents?  | 

22.  If  land  is  ten  dollars  an  acre,  how  many  acres  | 
can  a  man  buy  for  eighty  dollars  ? 

2H.  At  seven  dollars  a  yard,  how  many  yards  of 
cloth  can  be  bought  for  sixty-three  dollars? 

24.   How  long  will  it  takf  a  stage  to  go  seventy- 
fHo  miles,  if  it  goes  at  the  rate  of  eight  miles  an  ' 
hour  ? 


1 

SECTION   VI. 

ARABIC    NOTATION. 

fn  the  pieceding  lessons,  numbers  have  been  ex- 

fiessed  by  words.     In  business  calculations,  how-  | 

ever,  they  are 

commonly  denoted  by  the  following 

ten  characters  or  figures  ;  viz :                                     || 

1      2       3 

4      5     6       7        8        9        0 

one,    two,    three 

,    feur,    five    Bix,    aeren,    eight,    nine,    n»aght.* 

To  express 

len,  we  use  1  and  0,  thus  10  ;  to  ex- 

press  eleven^ 

we  use  two   Is,  thus  11  ;   to  express 

twelve^  we  use  1   and  2,  thus  12  ;  and  so  on,  as  in  || 

the  foliowing 

TABLE. 

!    l,one. 

21,  twenty-one. 

41,  forty-one. 

%  two. 

22,  twenty-two. 

42,  forty-two. 

i    3,  three. 

2;i,  twenty-three. 

43,  forty-three. 

4,  four. 

24,  twenty-four. 

44,  forty- four. 

i    5,  five. 

2,5,  twenty-five. 

45,  forty-five. 

1    (i,  six. 

'^\,  tw.nty-Kix. 

46.  forty-six,  SiC. 

1    7  «evcn. 

27,  twenty-seven. 

50.  fifty. 

j    ^.  exgUi. 

2H,  twenty-eight. 

51,  fifty-one,  &c. 

j    9,  nin«. 

21).  twenty-nine. 

HO,  sixty. 

\  10,  ten. 

30,  thirty. 

61,  sixty-one,  &c. 

j  11,  tJeven, 

31,  thirty -one. 

70,  seventy. 

I  12,  twflve. 

32,  thirty-two. 

71,  seventy-one,  &c. 

■  13,  thirteen. 

33,  thirty-three. 

80,  eighty. 

14,  fourteen!. 

34,  thirty -four. 

81,  eighty-one,  &c. 

15^  fifteen. 

35,  thirty-five. 

90,  ninety. 

16,  sixl*M»n. 

St),  thirty-sii. 

91,  ninety -one,  &c. 

17,  seventeen. 

37,  thirty-seven. 

100,  one  hundre*!.            j 

IK  njjhter.n. 

:W.  thirty-eight. 

200,  two  hunJntl.            ! 

ii^.  nineteen. 

3l»,  thirty-nine. 

500,  three  hundred,  &c.   1 

2^   twenty. 

40,  forty.                   ,  1000,  one  thou^Mi,nd.          | 

•  Th*-  pupil  sha  . 

d  be  able  to  distiincuinh  and  to  tpnte  these  ten  flarure*,   : 

b»fo!>>  I..X  attfmvt*  fc 

p  ••sj»itw;  larpsr  nunjh^r*      By  a  frw  hlntu  frtm    ti> 

r^Micber  mi  to  th^  cua 

Lnn^T  of  ccmbintng  th«m,  he  will  eaaily  ieam  vO  ex 

pr«w  any  namb«.r. 

i 

NOTATION. 


71 


ROxMAN    NOTATION. 
Another  method  of  expressing  numbers  is  by  tho 
follovvin^r  letters;   viz:   I,  V,  X,  L,  C,  D,  M.   'The 
rriBnner  of  doin^  this  may  be  learned  from  tne  fol- 
lowing 

TABLE. 


I  denotes  one 

XXX  denote  thirty. 

II 

i( 

two. 

XL 

(1 

forty 

III 

(( 

three. 

L 

IC 

fifty 

IV 

(( 

four. 

LX 

It 

sixty. 

V 

(i 

five. 

LXX 

" 

seventy. 

VI 

(( 

six. 

LXXX 

" 

eiirlity. 

VII 

(( 

eleven. 

xc 

" 

ninety. 

VIII 

'< 

eight. 

c 

" 

one  hundred. 

IX 

" 

nine. 

CI 

u 

one  hunil red  nnd  one. 

X 

1« 

ten. 

ex 

(1 

one  hundred  and  ten. 

XI 

u 

eleven. 

CO 

i( 

two  hundred. 

XII 

C( 

twelve. 

ccc 

(( 

three  hundred. 

Xlil 

l( 

thirteen,^ 

cccc 

<l 

four  hundred. 

XJV 

(( 

fourteen'. 

I) 

(( 

five  hundred, 

XV 

(( 

fifteen. 

DC 

II 

six  hundred. 

XVI 

(( 

sixteen. 

DCC 

<< 

seven  hundrinl. 

XVll 

II 

seventeen. 

DCCC 

l< 

eijfht  hundred. 

XVIII" 

eighteen. 

IXJCCC 

u 

nine  hurulred. 

XIX 

'» 

nim^leen. 

M 

II 

one  lhi)Usand. 

XX 

(( 

twenty. 

MC 

(1 

one  thou^^and  v.^^  one  hund. 

XXI 

(1 

twenty-one. 

MI) 

(I 

one  thousand  iV  fivehund 

XXII 

II 

twenty-two. 

MDCCCXLVI,   one    ihoufiand    eijfhi 

hundrev.  and  forty-six. 

EXERCISES    IN    NOTATION. 


I.   Write  the  following  numbers  in  figures  U}w  r? 
your  slate,  or  black-board  : 
1.    Kleven. 


3.  TMenty-one. 

5.  Forty -seven. 

7.  Spventv-ei^ht. 

9.  Si.xty-five. 

11.  Eighty-nine. 


2.  Seventeen. 

4.  Sixty. three. 

6.  Kiglily-six. 

8.  Kifiy-seven. 

10.  Niiiety-thre^i. 

12.  Ninety-hve. 


72  NOTATION. 


13.  One  hundred  and  one. 

14.  One  hundred  and  five. 

15.  One  hundred  and  seven. 

16.  One  hundred  and  ten. 

17.  Two  hundred  and  fourteen. 

18.  Four  hundred  and  twenty  three. 

19.  Three  hundred  and  nineiy-five. 

20.  Three  hundred. 

21.  Two  hundred  and  thirty. 

22.  Six  hundred. 

23.  Four  hundred  and  fifty-five. 

24.  Seven  iiundred  and  sixty. 

25.  Ki^^ht  hundred  and  sixty-five. 

26.  Nine  hundred  and  eighty-seven. 

27.  One  thousand. 

1.  Q.    What  is  the  an  of  expressing  numbers,  by 
t;i;ures  and  h'Hers,  called  i 

A71S.    It  is  calhid  iNotation. 

2.  Q.    What  is  the  method  of  expressing  numbers 
by  figures,  called  ? 

Ans.   The  Arahic  Notation. 

3.  Q.   Why  is  it  called  tiie  Arabic  notation. 
Ans.   Because  it  was  invented  by  the  Arabians. 

4.  Q.    VV'.at  is  the  method  of  expressing  numbers 
by  letters,  called  ? 

Ans.  The  Rivnian  Notation. 

5.  Q.    Why  is  it  called  the  Roman  Notation? 
Ans.   Because  it  Mas  invented  by  the  Rymans. 

6.  Q.    Which  of  the  alM)ve  systems  of  Notation,  is 
commonly  used  1 

Ans.   The  Arahic  Notation. 

7     Q.   What  is  the  art  of  reading   numbers  ex- 
pressed by  figures,  called? 

Ans,   It  is  called  Numeration. 


1 





1\ 

1 

1 

NOTATION. 

i 

EXERCISES 

IN  NUMERATION.              | 

Read  the 

numbers 

expressed  by 

the  iDliowing  , 

figures : 

13 

57 

10() 

310 

17 

39 

101 

295 

25 

76 

119 

430 

52 

48 

116 

375 

36 

79 

107 

537 

1       "^1 

91 

121 

426 

'     m 

37 

110 

111 

27 

81 

130 

239 

19 

65 

126 

685 

43 

58 

140 

491 

34 

83 

129 

507 

56 

89 

105 

810 

41 

92 

150 

740 

65 

78 

162 

936 

24 

94 

201 

845 

68 

86 

214 

987 

73 

98 

196 

1000       1 

1   Read  the 

numbers 

expressed  by 

the  followinf» 

figures : 

1845 

1850 

1«55 

1^60 

2167 

4101 

6705 

6200 

578 

5060 

7039 

7000 

1     2861 

2805 

4000 

6203 

1     3420 

6729 

7210 

8000 

1     1605 

2508 

6400 

8400 

4(J8 

3091 

1601 

7609 

4376 

2930 

8700 

3491     i 

2024 

6238 

4890 

9000     1 

5230 

7304 

5000 

8468     ) 

j     1040 

7490 

8245 

9999     j 

74  MISCELLANEOUS 


MISCELLANEOUS    EXAMPLES. 

1.  James  bought  a  lemon  for  4  cents,  and  a  pouud 
of  figs  for  8  cents :  how  much  did  he  pay  for  both  ? 

j  Solution. — 4  cents  and  8  cents  are  1 2  cents.  Tbero- 
I  fore,  if  he  paid  4  cents  for  his  lemon,  and  8  cents  for 
I  his  figs,  he  must  have  paid  12  cents  for  both. 

2.  A  man  bought  a  pound  of  tea  for  4  shillings, 
and  a  gallon  of  molasses  for  3  sbiUings :  how  many 

I  shillings  did  he  pay  for  both  ? 

3.  Uorace  })aid  6  cents  for  some  marbles,  3  cents 
fo^  a  top,  and  1  cent  for  a  whis».'e :  how  many  cents 
did  he  pay  for  all  i 

I      4.  How  many  are  5  and  13  ?  22  and  4  ?  3  and  16  ? 
4  and  13! 

5.  Uow  many  are  6  and  12 1  5  aU  14  ?  4  and  17  ? 
16  and  5? 

6.  llow  much  will  three  oranges  cost,  at  4  cents 
apiece  ?  *^- 

Analysis. — If  1  orange  costs  4  cents,  3  oranges  will 
vv^t  three  times  as  much  :  and  3  times  4  cent^^  are  12 
cents.  Therefore  3  oranges,  at  4  cent*  apiece,  will 
cost  12  cents.  I 

7.  If  1  quart  of  strawberries  cost  6  cents,  what  will  ■ 
2  quarts  cost  ?     2  times  4  are  how  many  *  | 

8.  What  cost  3  barrels  of  flour,  at  5  dol  ars  a  bar- 
rel ?     4  barrels?     5  barrels?  ^  . 

9.  What  cost  10  lambs,  at  7  slillings  apiece  ?  i 

10.  What  cost  4  bushels  of  cr:  uberrie*)  at  3  dollars  ' 
a  bushel  ?     6  bushels  ?  j 

11.  What  cost  6  sheep,  at  4  dollars  a  Km'i  ? 

12.  What  cost  8  cords  of  wood,  at  3  doU^it  d^  <?.C'd ? 
7  cords  ?     10  cords?  | 


BXAMPLES.  15 


I  13.  How  many  are  7  times  3  ?  5  times  8  ?  6  times 
I  4  ?   4  times  8  «  i 

I      14.  Henry  had  9  apples,  and  gave  away  4 :  how 

many  had  he  left  ?  j 

I  Solution. — 4  apples  taken  from  9  apples  leave  6 
'.  apples.  Therefore  if  he  had  9  apples,  and  gave  away 
I  4,  he  must  have  had  5  left  ?  j 

I  15.  Sarah  had  10  peaches,  and  gave  away  3  :  how 
,  many  had  she  left  ?  I 

I      16.  If  you  have  12  marbles,  and  lose  5  of  them, 
i  how  many  will  you  have  left  ? 
I      17.  3  from  17  leaves  how  many  ?  5  from  18  ? 
18.  5  from   11   leaves  how  many  ?  6  firom  10?  7 

from  12  ?  8  from  13  ?  6  from  15  ? 
I      19.   William  bought  a  knife  for  18  cents,  and  sold 

it  for  5  cents  less  than  cost :  how  much  did  he  sell  it 

for? 

20.   How  many  yards  of  ribbon,  at  6  cents  a  yard, 

can  be  bought  for  30  cents  ? 

Anali/sis. — If  6  cents  will  buy  1  yard,  30  cents  will 

buy  as  many  yards  as  6   is  contained  times  in  30  : 

and  6  is  contained  in  30,  5  times.    Therefore,  30  cents 

wiU  buy  5  yards  of  ribbon,  at  6  cents  a  yard. 

21    How   many   bushels  of  corn,  at  4   shillings  a 

bushel,  can  a  man  buy  for  16  shilUngs? 

22.  If  I  have  18  peaches  to  give  to  6  boys,  how 
many  can  I  give  them  a})iece  ? 

23.  How  many  hats,  at  5  dollars  apiece,  can  you 
buy  for  20  dollars? 

24.  How  many  times  6  in  24  ?  In  30  ?  In  42  ? 

25.  How  many  times  4  in  28  ?  In  20  ?  In  36  ? 

26.  A  man  l>ought  8  yards  of  cloth,  at  3  dollars  a 
yard,  and  paid  for  it  in  tiour,  at  4  dollars  a  barrel :  how 
many  barrels  did  it  take  ? 


76  MISCELLANKOUS 


Sufi  j/eaHov  — Firet  find  how  much  tne  cloth  comes  to 
If  1  yard  is  worth  3  dollars,  8  yards  are  worth  8 
times  as  much  ;  and  8  times  8  dollars  are  24  dol- 
lars.  Now  it  will  manifestly  take  as  many  barrels 
of  flour  to  pay  for  the  cloth,  as  4  dollars  are  con 
rained  times  in  24  dollars  ;  and  4  in  24,  6  times 
Atis.  6  barrels. 

27.  A  farmer  bought  6  pounds  of  tea,  at  4  shil- 
lings a  pound,  and  paid  for  it  in  whtat,  at  8  shillings 
a  bushel  ;  how  many  bushels  did  it  take  ? 

28.  A  man  bought  a  cow  for  10  dollars,  and  sold 
it  for  16  dollars :  how  much  did  he  make  by  his 
bargain  ? 

2ii.  If  Horatio  buys  6  oranges,  at  8  cents  apiece, 
and  sells  them  again  for  4  cents  apiece,  how  much 
will  he  make  by  his  bargain  ? 

80.  In  5  limes  8,  how  many  times  10? 

81.  In  6  titnes  0,  how  many  times  4  ? 

82.  In  8  times  8,  how  many  times  6  ? 

!       88.   A  butcher  sold  8  pounds  of  beef  for  56  cents  : 

what  was  that  a  pound  ? 
i      84.   A  dairy-man  sold  10  pounds  of  butter  for  80 
I  cents :   how  much  did  he  get  a  pound  ? 
I       85.    A  fanner  sold    10    bushels  of  oats,  at   3  shil- 
I  lings  a  bushel,   and   took   7  yards  of  flannel,  at   4 

shillings  a  yard,  and  the  rest  in  money  :  how  much 
I  money  did  he  receive  ? 
I      86.   What  is  the  ditTerence  between  3  times  6,  and 

7  times  8  ? 
'.      87.    What   is  the  diflference   between   5  times  b 

and  4  times  ^  ? 

88.   In   21,  how    many  times   5,  and    how    many 
I  over?  Ans.  4  tiuies  and  1  over. 

39.   In  18  how  many  times  4,  and  how  many  over? 


EXAMPLES.  .  77 


40.  In  80,  how  many  times  7,  and  how  many  over  ? 

41.  In  87,  how  many  times  9,  and  how  many  over  ? 

42.  In  4.5,  how  mar.y  times  "i ,  and  how  many  over  ? 
48.  In  6f>,  how  ntany  times  9,  and  how  many  over  '? 
4l.  If  3  coals  cost  24  dollars,  how  much  will   1 

coat  cost  ? 

Solution. — If  8  coats  cost  24  dollars,  1  coat  will 
cost  as  many  dollars  as  8  is  contained  times  in  24 : 
and  8  is  contained  in  24,  8  times.  Ans.  8  dollars. 

j      45.   How  many  hats,  at  five  dollars  a  piece,  can 

I  be  bou^iit  for  85  dollars  ? 

46.  How  much  flour,  at  7  dollars  a  barrel,  can  a 
man  buy  for  42  dollars  ? 

47.  How  many  yards  of  cloth,  ai  9  dollars  a 
yard,  will  86  dollars  buy  ? 

48.  How  many  tons  of  coal,  at  8  dollars  a  ton, 
will  64  dollars  buy  ? 

49.  A  man  bought  8  pair  of  boots  at  8  dollars 
a  pair,  and  paid  for  them  in  flour,  at  6  dollars  a  bar- 
rel :  how  many  barrels  diJ  it  take  ? 

50.  If  you  buy  4  penknives  at  10  cents  apiece, 
and  pay  for  them  in  beechnuts,  at  5  cents  a  quart, 

!  how  many  quarts  will  it  take  ? 

I      51.  A  farmer  sold  6  pounds  of  butler  for  10  cents  i 

!  a  pound,  asid  took  his  pay  in  njolasses,  at  6  cents  a  | 

quart:   how  many  quarts  did  he  receive?  | 

1      .52.  When  wlu^ai  is  7  shiliin«rsa  bushel,  how  many 

bushels  can  be  boujrht  for  68  shillings  ? 
'      58.  Six  boys  found  a  purse  of  money  containing 
'  48  dollars,   W'hich  they  divided  among    themselves 

3<]ually  :  how  many  dollars  did  each  receive?  j 

54.   If  a  man  has  45  dollars,   how    many   whole 

barrels  of  flour  can  he  buy,  at  6  dollars  a  barrel,  and 

how  many  dollars  will  he  have  over  ? 


78  MISCELLANEOUS 


55.  Ai  5  dolla-s  a  yard,  how  many  whole  yards 
of  cloth  can  be  bought  for  28  dollars,  and  how  many 
dollari--  o>er  ? 

56.  In  85,  how  many  times  9,  and  how  many 
over? 

57.  In  107,  ho>*  many  times  10,  and  how  many 
over? 

58.  In  95,  how  many  times  9,  and  how   many 
I  over? 

59.  In  83,  how  many  times  8,  and  how  man) 
over  ? 

60.  In  109,  how  many  times  10.  and  how  many 
over  ? 

61.  Henry  bought  a  Geography  for  5(>  cents,  and  a 
Reader  for  20  cents  :  h  jw  much  did  he  give  tor  both  ? 

Analysis. — 50  is  equal  to  5  tens,  and  20  is  equal 
to  2  tens :  now  5  tens  and  2  tens  are  7  tens ;  and 
7  tens  are  equal  to  70.      Ans.  7(^  cents. 

62.  How  many  tens  in  30  ?   In  70  ? 

63.  How  many  tens  m  40  ?   In  90  ? 

64.  How  many  tens  in  80  ?   In  100  ? 

65.  4  tens  are  equal  to  how  many  ? 

66.  6  tens  are  equal  to  how  many  ? 

67.  7  tens  are  erjual  to  how  many  ? 

68.  9  tens  are  equal  to  how  many  ? 

69.  8  tens  are  equal  to  how  many  ? 

70.  10  tens  are  equal  to  how  many  ? 

71.  3  tens  and  5  tens  are  how  many? 
Solution, — 3  tens  and  5  tens  are  8  tens     and  8 

tens  are  equal  to  80. 

72.  6  tens  and  4  tens  are  how  many  ? 

73.  How  many  are  30  and  50  ? 

74.  How  many  are  60  and  30  ? 

75.  How  many  are  40  and  40? 


EXAMPLES.  79 


76.  Henry  bought  30  marhles,  atuJ  his  uncle  gave 
him  40  more  :   how  many  marbles  had  he  then  ? 

77.  If  a  pound  of  lea  costs  M  cents,  and  a  g^allon 
of  molasses  40  cents,  how  much  will  both  oaxl 

78.  A  man  gave  40  dollars  for  a  ran,  ar^  50 
!  dollars  for  a  yoke  of  oxen  :  how  much  did  he  j,ive 
j  for  both  ? 

I      79.   A  farmer  sold  a  horse  for  90  dollars,  and   a 

cow  for  30  dollars  :  how  much  did  he  get  for  both  ? 
I     Analysis. — 90  is  equal  to  9  tens,  and  30  is  equal 

to  3  tens  :  9  tens  and  3  tens  are   12  tens;  and   12 
!  lens  are  equal  to  120.     Aiis.   120  dollars. 
j      80.  James  gave  60  cents  for  a  sled,  90  cents  for 

a  pair  of  skates,  and  8  cents  for  a  knife:  how  much 

did  he  give  for  all  ? 

81.  If  a  man  travels  70  miles  the  first  day,  and 
40   the   next  day,   how  far  will  he  travel   in  both 

I  days  ? 

82.  Harriet  gave  25  cents  for  her  ReadfTr,  and 
37  cents  for  her  Practical  Arithmetic:  how  much 
did  she  give  for  both  ? 

Analysis. — 25  is  composed  of  2  tens  and  5  units, 
and  37  is  composed  of  3  tens  and  7  units :  now  2 
lens  and  3  tens  are  5  tens  or  50  ;  and  5  units  and  7 
units  are  12  units,  which  added  to  50  make  62, 
^iis.   62  cents. 

83.  I  low  many  are  32  and  45  ? 

84.  How  many  are  56  and  ?H  ? 

85.  How  many  are  72  and  47  ? 

86.  How  many  are  61  and  82  ? 

87.  A  man  bought  a  horse  for  75  dollars,  and  a 
buggy  for  63  dollars  :  how  much  did  he  pay  for 
both  ?  ; 

88.  A  farmer  raised  54  bushels  of  corn  on  one  I 


8^)  MISCELLANEOUS 

acre,  and  48  bushels  on  another  :  how  many  bush- 
els dii  he  raise  on  both  acres  ? 

89.  A  man  gave  90  cents  for  a  bushel  of  wheal, 
and  40  cents  for  a  buahol  of  rye  :  how  much  more 
did  he  pay  for  his  wheat  than  for  iiis  rye  ? 

Solution. — 90  is  9  tens,  and  40  is  4  tens  :  now  4 
tens  from  9  tens  leave  5  tens  ;  and  5  tens  are  equal 
to  50.     Ans.  50  cents. 

90.  Frank  gave  80  cents  for  a  Dictionary,  and  50 
cents  for  a  Geography  :  how  much  more  did  he  pay 
for  his  Dictionary  than  for  his  Geography? 

91.  William,  having  100  cents,  spent  60  of  them : 
how  many  cents  had  he  left  ? 

92.  If  ►^a.  ah  reads  80  pages  in  a  day,  and  Susan 
reads  50,  hew  many  more  pages  will  Sarah  read 
than  Susan  ? 

98.  A  man  put  75  sheep  into  a  pastidre,  but  20  of 
them  jumped  out :  how  many  remauied  in  the  pas- 
ture ? 

94.  25  from  45  leaves  how  many  ? 

95.  36  from  76  leaves  how  ;i>any  ? 

96.  72  from  85  leaves  how  many  ? 

97.  63  from  79  leaves  how  many  ? 

98.  84  from  97  leaves  how  many  ? 

99.  A  farmer  sold  5  cows,  at  30  dollars  a  head  : 
how  much  did  they  come  do  ? 

Aruilyais. — If  1  cow  costs   30   dollars,  5  cows  will  ; 
cost  5  times  as  much.     Now  30  is  equal  to  3  tecs,  and 
6  times  3  tens  are  15  tens;  and   15  tens  are  equal  to 
150.     Therefore,  5  cows,  at  30  dollars  a  head,  will  cost ; 
150  dollars. 

100.  What  cost  20  sheep,  at  8  shillings  a  head?      ! 

101.  A  dairy- woman  sold  40  pounds  of  cheese  for  7  j 
cents  a  |x>und :  how  much  ».lid  it  come  to  ? 


KXAMPLE8.  81 

102.  A  merchant  sold   60   pounds  of  sugar  for  8 
cotits  a  pound  :  how  much  did  it  come  to? 
!       103.  A  manufacturer  sold  100  yar^ls  of  muslin,  at 
I  9  c«nts  a  yard  :  how  much  did  it  con  e  to  ! 

104.  What  cost  3  melons,  at  15  cc  nts  apiece  ? 
Awilysis. — If  1  melon  costs  15  ceuts,  3  melons  will 

cost  >t  times  as  much.  Now  15  is  composed  of  10 
and  5  :  but  3  times  10  are  30,  and  3  times  5  are 
15 ;  and  15  added  to  30  make  45.  Therefore  3  mel- 
ons, at  t5  cents  aj^iece,  will  cost  45  cents. 

105    What  will  4  slates  cost,  at  14  cents  apiece  ? 

106.  vVhat  cost  5  pounds  of  butter,  at  16  cents  a 
pound  ? 

107.  What  will  Y  yards  of  cloth  come  to,  at  15 
shillings  a  yard  ? 

105.  A.  farmer  sowed  6  acres  of  oats,  which  yielded 
25  bushels  per  acre  ;  how  many  bushels  of  oats  did 
he  have  ?         ^-- 

Analysis. — 25  is  composed  of  2  tens  and  5  units  : 
now  6  times  2  tens  are  12  tens,  or  120,  and  6  times 
5  are  30;  and  30  added  to  120  make  150.  There- 
fore 6  acres  will  yield  150  bushels,  at  25  bushels  per 
acre? 

109.  At  35  dollars  apiece,  how  much  will  5  acres 
'^^  land  cost  ? 

110.  At  42  dollars  apiece,  how  much  will  7  sleighs 
cost  ? 

111.  Joseph  bought  7  oranges,  at  4  cents  apiece, 
and  sold  them  at  5  cents  apiece :  how  much  did  he 
make  by  his  bargain  ? 

Sng^jestion. — The    learner    should    first    find    how 

!  much   he  paid  for  the  oranges,  then  how  much  he 

received  for  them;  finally,  taking  the  sum  he  pail 


82  MISCELLANEOUS 


from  the  sum  he  received,  the  remainder  will  be  his 
gain. 

112.  A  man  bought  10  sheep  at  7  shillings  a 
head,  and  sold  them  again  at  9  shillings  a  head : 
how  much  did  he  gain  by  the  bargain  ? 

113.  A  merchant  bought  "i  barrels  of  flour,  at  9 
dollars  a  barrel,  and  sold  them  at  ()  dollars  a  barrel :  j 
how  much  did  he  lose  by  his  bargain  ? 

114.  A  man  bought  6  hats  at  4  dollars  apiece, 
and  .5  yards  of  cloih  at  6  dollars  a  yard  :  how  much 
did  he  pay  for  both  ? 

115.  A  farmer  sold  7  pounds  of  veal  at  8  cents  a 
pound,  and  4  pounds  of  butter  at  b  cents  a  pound  : 
how  much  did  he  receive  for  both  ? 

116.  If  1  buy  8  pounds  of  sugar  at  7  cents  a 
pound,  and  10  lemons  at  »i  cents  apiece,  how  much 
must  I  pay  for  both  ? 

117.  If  5  boys  can  saw  a  cord  of  wood  in  4  hours, 
how  long  will  it  take  1  boy  to  saw  a  cord  ? 

118.  If  10  men  can  do  a  job  of  work  in  20  dajs, 
how  long  will  it  take  one  man  to  do  it  ? 

110.  If  a  barrel  of  flour  will  last  6  men  15  days, 
how  long  will  it  last  1  man  ?  I 

120.  If  6  men  can  dig  a  cellar  in  4  days,  how  j 
many  men  will  it  lake  to  dig  it  in  1  day  ?  \ 

ril.  James  divided  100  oranges  equally  among! 
10  companions:  how  many  oranges  did  he  give  to! 
each  ?  ! 

122.  A  man  paid  63  dollars  for  9  yards  of  cloth  :  | 
how  much  was  that  a  yard  ?  v     | 

123.  A  farmer  sold  9  lambs  for  72  shillings:  how  ' 
much  did  he  receive  apiece  ? 

124.  A  merchant  sold  9  hats,  at  4  dollars  apiece, 


EXAMPLES.  d3 


and  agreo  I  to  take  his  pay  in  flour  at  6  dollars  a  bar- 
rel :  hoA*  many  barrels  did  he  receive  for  his  hats? 

125.  A  cobbler  sold  8  pair  of  boots  at  5  dollars  a 
pair,  and  tooli  4  tons  of  coal  worth  9  dollars  a  ton, 
and  the  rest  in  cash :  how  much  cash  did  he  re- 
ceive ? 

126.  How  many  bunches  of  quills  can  I  purchase, 
at  8  cents  a  bunch,  for  12  slates  worth  6  cents  apiece  ? 

127.  In  7  times  8,  how  many  times  6,  and  how 
many  over? 

128.  In  9  times  5,  how  many  times  7,  and  how 
many  over  ? 

129.  In  7  times  9,  how  many  times  6,  and  how 
many  over  ? 

130.  In  8  times  9,  how  many  times  10,  and  how 
many  over  ? 

131.  In  10  times  6,  how  many  times  7,  and  how 
many  over  ? 

1.S2.  In  8  times  10,  how  many  times  9,  and  how 
many  over  ? 

133.  In  9  times  9,  how  many  times  8,  and  how 
many  over  ? 

134.  In  8  times  7,  how  many  times  10,  and  how 
many  over  ? 

13.5.  In  S  times  8,  how  many  times  7,  and  how 
manv  over  ' 

I'dii.  Charles  bouj[yht  a  history  for  27  cents,  a  ilate 
for  10  cent^  less,  hikI  a  geograpliy  for  10  centa  more; 
ibaii  his  history:    how  much  did  he  pay  for  all?  i 

137.  llt'nry  had  3  ap})les,  (xporge  had  4  times  as 
many  as  lienrv,  and  William  had  twice  as  many  as 
t)oth:  how  many  did  George  and  William  have^ 
apiece  ;  and  how  many  had  all  of  them  ?  i 


SECTION   VII. 

FRACTIONS. 
LESSON  I. 

1.  If  I  divide  any  number  or  thing,  as  an  apple 
or  a  pear,  into  two  equal  parts,  what  is  each  of  those 
pans  called  ? 

Ans.     One  half. 

2.  What  is  then  meant  by  one  Imlf? 

3.  I  low  many  halves  make  a  w/io/e  one  ? 
Ans.    Two. 

4.  If  I  cut  a  sheet  of  paper  into  halves  and  give 
,  you  1  half,  what  part  of  the  sheet  shall  I  have  left  ? 
j  U  1  give  you  2  halves,  how  much  would  be  left? 

Note. — The  meaning  of  the  terms  one  half,  one  third,  one 
'  fourth,  &.C..,  flhouKl  l)e  illustrated  to  tlie  pupil  by  artnally  cutting 
I  some  familiar  object,  as  an  apple  or  a  {»ear,  into  kuhex,  thirds, 
j  fourths,  &c.  In  this  way,  he  will  easily  citrnprehnnd  the  mean- 
;  ing  of  the  terms  used  in  fractions,  and  will  lie  able  to  perform 
j  operationu  in  them  with  as  much  fatiliiy  aa  in  whole  nurabcra. 

j       5.   If  any  number  or  thing  is  divided  into  three 

equal  parts,  what  is  each  of  the  parts  called  ? 
!       Ans.    One  third. 

6.  What  then  is  meant  by  (me  third?  What  is 
meant  by  two  thirds  ? 

7.  If  1  cut  an  apple  into  thirds  and  give  away  1 
third,  what  pan  will  be  left  ?  If  I  give  away  2  thirds, 
what  part  will  be  left  ? 

8.  How  many  thirds  make    a  whole  one? 

9.  If  a  number  or  thing  is  divided  intoybu*-  equal 
parts,  what  is  each  of  the  parts  called  ? 

i       Atis.   One  fourth,  or  one  quarier. 

I       10.   What  is  meant  by  2  fourths?   By  3  fourth*? 


FRACTIONS. 


85  I 


11  If  you  divide  a  stick  of  candy  in  fourths,  and 
give  3  fourths  of  it  to  your  companions,  what  part 
of  it  would  you  have  left? 

12.  If  you  give  away  1  fourth,  what  part  would 
be  left  ?  I 

13.  Tv'o  fourths  and  one  fourth  make  how  many  | 
fourths  ?  Three  fourths  and  one  fourth,  make  how  j 
many  fourths  ?  i 

14.  How  msiny  fourths  make  a  whole  one  ?  , 

LESSON    II. 

1.  What  is  meant  by  1  fifth  ?  I 
Ans.   When  any  thing  is  divided  into  Jine  equal  \ 

parts,  one  of  these  parts  is  called  1  fifth.  | 

2.  What  is  meant  by  2  fifths?     By  3  fifllis  ?    B>   i 

4  fifths  ? 

3.  If  you  cut  a  pie  into  fifths,  and  take  away  2 
fifths,  how  many  fifths  will  remain  ? 

4.  3  fifths  and  2  fifths  make  how  many  fifths  ? 

5.  How  many  Jiff  hs  make  a  whole  one? 

0.   What  is  ojeant  by  1  sixth  ?    By  2  sixths  ?    By 

5  sixths  ?   By  3  sixths  ? 

7.  James  had  2  sixths  of  a  dollar,  and  his  father 
gave  him  3  sixths  more :  what  part  of  a  dollar  had 
he  then  ? 

I      8.  How  many  sixtJis  make  a  whole  one  ? 

,       9.  What  is  meant  by  1  seventh  ?  By  2  sevenths  ? 

•  By  3  sevenths  ?  By  5  sevenths  ? 

10.  What  part  of  a  dollar  will  2  sevenths  and  4 
sevenths  make  ? 

I       11.   A  man  hoed  3  sevenths  of  an  acre  of  corn  in 

i  one  day,  and  2  sevenths  of  an  acre  the   next  day  . 

!  what  part  of  an  acre  did  he  hoe  in  boLn  days? 


86  FRACTIONS. 


12.  How  many  seventJis  make  a  whole  one  ? 
11^.   What  is  meant  by  1  eighth?  By  2  eighths? 
By  8  eighths  ?  By  5  eighths  ?  By  7  eighths  ? 

14.  How  many  eighths  make  a  whole  one? 

15.  What  is  meant  by  1  ninth  ?  By  2  nitiths  ?  By 
8  ninths  ? 

16.  How  many  ninlhs  make  a  whole  one  ? 

17.  What  is  meant  by  3  tenths?  By  5  tenths? 
By  7  tenths  ?    *    • 

18.  What  is  meant  bv  1  fifteenth  ?  By  2  fifteenths  ? 
By  8  fifteenths  ?   By  7''fifteenths  ?   By  10  fifteenths  ? 

19.  What  is  meant  by  1  twentieth  ?  By  2  twenti- 
eths ?   By  8  twentieths?   By  12  twentieths? 

20.  How  many  thirtieths  make  a  whole  one  ?  How 
ma.ny  forty -fifths  make  a  whole  one  ?  How  many 
sixty  fourths  make  a  whole  one  ?  How  many  hun- 
dredths make  a  whole  one  ? 

I  LESSONIII. 

1.  If  one  half  of  a  pear  costs  1  cent,  how  much 
will  two  halves  or  a  whole  pear  cost  ? 

Suggestion. — 2  halves  or  a  whole  pear  will  cost 
twice  as  much  as  1  half.  Now  if  1  half  costs  1  cent, 
2  halves  or  a  whole  one  will  cost  2  times  1  cent,  and 
2  times  1  cent  are  2  cents.     Ans.   2  cents. 

2.  If  1  half  an  orange  costs  2  cents,  how  much  | 
will  a  whole  orange  cost  ?  i 

8.  If  i  half  a  yard  of  ribbon  costs  3  cents,  what  i 
will  a  whole  yard  cost  ?  j 

4.  If  1  third  of  a  pie  costs  2  cents,  how  much  will  | 
2  thirds  of  a  pie  cost  ?  How  much  will  3  thirds  or  I 
a  whole  pie  cost  ?  I 

5.  If  1  fourth  of  a  poui.d  of  sugar  costs  2  cenjs,  j 


FRACTIONS.  87   I 


how  much  will  2  fourths  cost  ?  3  fourths  ?  A  whole 
|x>und  ? 

6.  A  man  sold  1  fifth  of  a  cord  of  wood  for  3  shil- 
iinjTs :  how  much  would  3  fifths  come  to  at  the  same 
rate  ?     A  whole  cord  ? 

7.  If  I  sixth  of  a  barrel  of  flour  costs  1  dollar, 
how  much  will  4  sixths  of  a  barrel  cost  ?  6  sixths  ? 

S.   If  1  seventh  of  a  ton  of  hay  is  worth  2  dollars, 
what  is  8  sevenths  worth  ?  4  sevenths  ?  6  sevenths  ? 
I  7  sevenths  ? 

9.  If  1  eighth  of  a  yard  of  cloth  costs  1  dollar, 
how  much  will  5  eighths  cost  ?  3  eighths  I  7 
eighths  ?  8  eighths  ? 

10.  If  1  ninth  of  an  acre  of  land  is  worth  3  dollars, 
how  much  is  4  ninths  worth  ?  5  ninths?  7  ninths? 
H  ninths  ? 

11.  One  tenth  of  a  hogshead  of  molasses  is  worth 
3  dollars :  how  much  is  5  tenths  of  a  hogsheaii 
worth?  7  tenths  ?  9  tenths?  [low  much  is  a  hogs- 
head worth  ? 

LESSON    IV. 

1.  If  a  yard  of  tape  is  worth  2  cents,  how  much 

is  1  half  a  yard  worth  ? 
I       So/uf?on. — Since  a  whole  yard  is  worth  2  cents, 
I  1    half  of  a  yard  is  worth   1  half  as  much  :  and  I 

half  of  2  cents  is  1  cent.     Ans.   1  cent. 
I       2.   What  is  1  half  of  4  cents?    Ans.   2  cents. 
i       Why? 

i       Ans    If  4  cents  are  divided  into  two  equal   par^s, 
!  one  of  the  parts  is  2  cents. 

j       3.   If  an  r.*-ange  costs  4  cents,  how  much  will  half 
j  an  orange  cost  ? 


88  FRACTIONS. 


I  4.  What  is  1  half  of  6  cents  ?  What  is  1  half  of  I 
S  cents  ?  Of  10  cents  ?  Of  12  e-^.nts  ?  Of  l«  cents  ?  j 
Of  20  cents?  j 

I  5.  If  a  lemon  costs  6  cents,  how  much  will  1  third  \ 
of  a  lemon  cost  1   What  is  1  third  of  6  cents?  , 

e>.    What  is  1   third  of  9  cents  ?   What  is  1   third  I 
of  12  cents?  Of  18  cents?  Of  15  cents?  Of  24 
cents  ?  Of  :iO  cents  ? 

Observation. — From  the  preceding  examples,  the 
learner  will  perceive  that  a  half  o{  a  number  is  equal 
to  as  many  units  as  2  is  contained  times  in  that  num- 
ber ;  a  tkird  of  a  number  is  ecjual  to  as  many  units 

;  as  8  is  contained  times  in  that  number  ;   2i  fourth  of  a 
number  is  equal  to  as  many  units  as  4  is  contained  | 
times  in  that  number,  &c. 

7.  How  do  you  find  a  ha/f  of  a.  number  ? 
Ans.   Divide  the  number  by  2. 

8.  How  find  a  third  of  a  number?     How  find  a  ! 
fourth  of  a  number  ?  A  fifth  ?  A  sixth  ?  A  seventh  ? 

An  eighth  ?  A  ninth  ?   A  tenth  ? 

9.  What  is  1  fourth  of  12  dollars?  Of  16  dollars? 
Of  20?  Of  82?  Of  24?  Of  28?  Of  36  ?  Of  40? 

10.  If  a  ton  of  coal  is  worth  10  dollars,  what  is 
1  fifth  of  a  ton  worth  ? 

11.  What  is  1  fifth  of  15  dollars  ?  Of  20  dollars  ? 
Of  80?  Of  25?  Of  40?  Of  50?  i 

12.  What  is  one  seventh  of  7  ?  Of  14  ?  Of  28  ? 
Of  49?  Of  70?  I 

18.   What  is  one  eighth  of  16  ?  Of  24  ?  Of  40  ?  i 
Of  80?  Of  72?  i 

14.  VVhatisl  ninthof9?  Of  27  ?  Of  18  ?  Of  3b  ?  ! 
Of  45?  Of  72?  Of  90?  1 

15.  What  is  one  tenth  of  l()  ?  Of  8U  ?  Of  20?  Of! 
,60?  Of  50  ?  Of  100?  i 


FRACTIONS.  89 


LESSON    V. 

1.  llov  much  will  2  apples  cost,  at  1  half  a  ceni 
apiece  ? 

Solution. — Since  1  apple  costs  1  half  a  cent,  2  ap- 
ples will  cost  2  times  as  much  :  and  2  times  1  half 
are  2  halves,  or  a  whole  cent.      Ans.   1  cent. 

2.  What  cost  3  apples,  at  1  half  a  cent  apiece  ? 
So/uiion. — II'  1  apj)le  costs  1  half  a  cent,  3  apples 

will  cost  three  times  as  much,  or  3  halves  :  and  3 
halves  are  e(\uh  to  1  whole  cent  and  1  half.  Ans.  1 
cent  and  1  half. 

3.  At  1  third  of  a  dollar  a  bushel,  how  much  will 
6  bushels  of  oats  cost  ? 

4.  What  cost  2   pounds  of  tea,  at  3  fourths  of  a 
I  dollar  a  pound  ?     How  much  is  2  times  3  fourths  ? 

•'^.   In   8    fourths,    how   many    whole  ones  ?   In  9 
fourths,    how    many    whole  ones,    and    how    many 
fourths  over?   In  13  fourths?   In  15  fourths? 
I      6.   What  cost  3  yards  of  flannel,  at  2  fifths  of  a 
dollar  a  yard  ?   How  much  is  3  times  2  fifths  ? 

7.  In  10  fifths,  how  many  whole  ones?  In  12 
fifths  ?  In  15  fifths?  In  2(»  fifths  ?  In  32  fifths? 

8.  At  3  eighths  of  a  dollar  a  bushel,  how  much 
will  4  bushels  of  apples  come  to  ?  i 

9.  In  24  eighths,  how   many  whole  ones?  In  19  ! 
eighths  ?   In  33  eighths  ?  In  40  eighths  ?  I 

10.  At  7  tenths  of  a  dollar  a  pair,  how  much  will 
3  pair  of  gloves  come  to  ? 

11.  How  much  is  3  times  4  fifths  ? 

12.  How  much  is  4  times  6  eighths  ? 

13.  How  much  is  7  times  4  tenths? 

14.  How  much  is  5  timfs  7  ninths? 


90  FRACTIONS. 


LESSON    Vi  . 

'      1.   Wha.  ^art  of  2  cents  is  1  cent?     Ans.  1  half. 
'      Why? 

Ans.    Hocause,  if  we  divide  2  cents  into  ttm)  equal 

parts,  one  of  these  parts  is    1   cent ;  and   when  aay 
;  thing  is  divided  into  two  equal  parts,  one  of  these 

parts  is  called  1  lia/f. 

I      2.   What  part  of  3  cents  is  1  cent  ?   Why  ? 
I      3.    What  part  of  3  cents  is  2  cents  ? 
i      Solution. — Since  1  is  1  third  part  of  3,  2  is  2  times 
■  as  much  :  and  2  linuis  1  third  are  2  thirds.      Aiis.  2 

thirds, 
i      4.    What  part  of  3  is  4  ? 

Ans.  4  thirds  of  3,  which  are  equal  to  1  and    I 

third. 

5.  What  part  of  4  pears  is  1  pear?  What  part 
of  4  is  2  ?    Is  3  ?   Is  5  ?    is  8  ?    Is  9  ?   Is  12  ? 

6.  What  j>art  of  5  dollars  is  I  dollar?  What  part 
of  5  is  2  ?   Is  3  ?   Is  4  ?   Is  6  ?  Is  8  ?   Is  10  ?  Is  12  ? 

,  Is  15  ?   Is  20? 

j      7.   What   part  of  6  pins  is  1  pin  ?  What  part  of  i 

6  is  2  ?   Is  3  ?   Is  5  ?  Is  7  ?   Is  8  ?   Is  12  ?   Is  18  ? 

I      8.   What  part  of  8  apples  is  1  apple?   What  part 
of  8  is  2  ?  Is  3  ?   Is  5  ?   Is  7  ?   Is  16  ?  Is  20  ? 
I      9.   What  part  of 7  days  is  1   day?   What  part  of 

7  is  2  ?   Is  3  ?  Is  6  ?   Is  8  ?   Is  14  ?   Is  18  ? 

10.  What  part  of  10  nuts  is  1  nut  ?  What  part  of 
10  is  2  =    Is  5?   Is  3?   Is  25?   Is  30  ?   Is  35? 

11.  What  part  of  12  ponce  is  1  penny  ?  What 
part  of  12  is  2  ?  Is  3  ?  Is  6  ?  Is  18?  Is  24  ?  Is  28  ? 
Is  30?   Is  47? 

12.  U'hat  part  of  16  ounces  is  1  ounce?  What 
part  of  16  is  2?  Is  5  ?  Is  10?  Is  12  ?  Is  16?  Is  18? 
Is  25  ? 


FRACTIONS.  91 


13.  What  part  of  20  sliillings  is  1  shilling  ?  What 
pan  of  20  is  3  ?    Is  7  ?    Is  10  ?    Is  40  ? 

14.  What  part  of  30  is  1  ?  Is  2  ?  Is  5  ?  Is  26  ?  Is 
36  ?    Is  48  ?  I 

15.  What  part  of  100  is  U  Is  3  !  Is  10?  la  60? 
Is  73?    Is  85? 

LESSON    VII. 

1.  If  you  buy  an  orange  for  4  cents,  what  part  of 
an  orange  can  you  buy  for  1  cent  ? 

Analysis. — 1  cent   is  1   fourth    part    of   4   cents  ; 
therefore  1  cent  will  buy  1  fourth  as  much  as  4  cents. 
But  4  cents  will  buy  a  whole  orange  ;  consequently  i 
1  cent  will  buy  1  fourth  |>art  of  an  orange. 

2.  At  6  shillings  a  pound,  what  part  of  a  pound  of  | 
tea  can  be  bought   for  1  shilling  ?     Foe  2  shillings  ? 
For  3  shillings  ?     For  6  shillings  ? 

3.  At  8  cents  a  pound,  what  part  of  a  pound  of 
saleratus  can  you  buy  for  1  cent  I     For  2  cent**  ?    For  ! 
3  cents  ?     For  5  cents  ?     For  7  cents  ?     For  6  cents  ? 
For  8  cents  ? 

4.  Seven  days  make  a  week :  what  part  of  a  week 
is  1  day  ?  What  part  of  a  week  is  2  days  ?  3  days  ? 
6  days?     5  days? 

5.  At  8  cents  a  yard,  what  part  of  a  yard  of  calico 
can  you  buy  for  1  ceirt  ?  For  5  cents?  For  6  cents  ? 
For  7  cents  ? 

6.  At  6  cents  a  ya?  d,  how  much  calico  can  you  buy 
for  7  cents  ? 

Analysis. — Since  6  cents  will  buy  1  yard,  1  cent 
will  buy  1  sixth  of  a  yard;  and  7  cents  will  buy  7 
times  as  much  :  now  7  times  1  sixth  Is  7  sixths,  equal 
to  1  whole  one  and  1  sixth.  Therefore  7  cents  will 
buy  1  and  1  sixth  yard  of  calico,  at  6  :ents  a  yard. 


92  FRACTIONS. 


Y.  At  5  cents  a  yard,  what  part  of  a  yard  of  silk 
braid  can  you  buy  fur  1  cent  ?  How  much  can  you 
buy  ^Jr  d  cejjts  ?      For  6  cents  ?     For  10  cents  ? 

8.  At  10  dollars  an  acre,  what  part  of  an  acre  of 
land  can  vou  buy  fur  1  dollar  ?  For  3  dollars  ?  Foi 
12  dollars?     For  1 5  dollars ?     For  20  dollars  ?  , 

9.  Vv  nat  part  of  a  pound  of  buiter,  at  12  cents  a 
pound,  can  be  bought  for  1  cent  ?     For  5  cents  I     F^or  , 
15  cents  f  I 

10.  At  15  cents  a  pound,  what  part  of  a  pound  ot  [ 
figs  can  you  buy  for  1  cent  ?     For  16  cents? 

1 1.  Twenty  shilling  make  a  pound  :  what  part  of  a 
pound  is  1  shilling?  2  shillings?  15  shillings  ?  20 
shiiUngs?     22  shillings?     30  shillings  ?  j 

LESSON    VIII.  I 

1.  What  will  2  oranges  cost,  at  3  and  1  half  cents  i 
apiece  ?  | 

Analysis. — If  1  orange  costs  3  and  1  half  cents,  2 
oranges  will  cost  twico  as  much.  Now  2  times  3 
cents  are  6  cents,  and  2  times  1  half  are  2  halves, 
equal  to  1  cent,  which  added  to  6  cents,  makes  7  cents. 
Therefore  2  oranges,  at  3  and  I  half  cents  apiece,  will : 
cost  7  cents. 

2.  What  will  5  yards  of  tape  cost,  at  2  and  1  third 
cents  a  yard  ?  j 

Analysis. — Since  1  yard  of  tape  costs  2  and  1  third  | 
cents,  5  yards  will  cost  5  times  as  much :  now  6  times 
2  ctm^s  a-e  1 0  cents ;  and  5  times  1  third  are  5  thirds, 
equal   to    1   cent  and   2   thirds,   which   addec   to   10  ■ 
cents,   make  1 1   and    2    thirds    cents.      TLorefore    5 
yards  of  tape,  at  2  and  1  third  cents  a  yard,  will  cost  | 
1 1  and  two  thirds  cents.  i 


FRACTIONS.  93 


4.  What  cost  6  yards  of  cloth,  at  2  and  1  half 
dollars  per  yard  ?  How  much  is  6  times  2  and  1 
half? 

5.  At  3  shillings  a  yard,  what  will  4  and  2  thirds 
yards  of  ribbon  come  to  1 

6.  Sarah  bought  8  and  3  fourths  yards  of  cash- 
mere, at  4  shillings  a  yard  :  how  much  did  it  come  to  1 

7.  A  farmer  bought  10  sheep,  at  2  and  1  third 
dollars  a  head :  how  much  did  they  come  to  ? 

8.  In  1  rod  there  are  5  and  1  half  yards  :  how 
many  yards  are  there  in  8  rods  ? 

9.  How  much  is  5  times  4  and  3  fourths  ? 

10.  How  much  is  7  times  6  and  4  sevenths  ? 

1 1 .  How  much  is  6  times  4  and  3  ninths  ? 

1 2.  How  much  is  8  times  5  and  5  sixths  ? 

LESSON    IX. 

1.  If  1  Narrel  of  flour  costs  9  dollars,  how  much 
will  2  thirds  of  a  barrel  cost  ? 

Suggestion. — Fii-st  find  the  cost  of  1  third,  then  of  2 
thirds.  (See  Observation,  p.  88.) 

If  one  barrel  costs  9  dollars,!  third  of  a  barren! 
will  cost  1  third  of  9  dollars.  Now  1  third  of  9 
dollars  is  3  dollars,  and  2  thirds  will  be  twice 
as  much  ;     and    2    times  3    dollars  are  6    dollars. 

Ans.  6  dollars. 

2.  If  1  yard  of  cloth  costs  6  dollars,  how  much 
will  2  thirds  of  a  vard  cost  ? 

I  3.  How  much  i's  2  thirds  of  0  ?  Of  9  ?  Of  12  ?  ! 
i  4.  If  a  pie  costs  12  cents,  what  will  3  fourths  of  ' 
i  a  pie  cost  ?     Hcv  much  is  3  fourths  of  12? 

5.  How  n  uch  will  2  fifths  of  a  ton  of  coal  coet,  i 

at  10  dollars  a  ton  '?  How  much  will  4  fifths  ot  a 

ton  cost  1 


94  FRACTIONS. 


6.  How  much  will  3  sevenths  of  an  acre  of  lar  d 
cost,  at  21  dollars  per  acre  ? 

7.  If  a  ton  of  hay  costs  16  dollars,  what  will 
5  eighths  of  a  ton  cost  1 

8.  If  a  drum  of  figs  costs  18  shillings,  how  much 
will  2  ninths  of  a  drum  cost  ?  4  ninths  ? 

9.  At  20  shillings  a  barrel,  how  much  will 
4  fifths  of  a  barrel  of  cider  cost  ? 

10.  How  much  is  3  fourths  of  4  ?  Of  8?  Of  16  ? 

11.  How  much  is  5  sevenths  of  14?  Of  21  ? 

LESSON    X. 

1 .  Q.  When  a  number  or  thing  is  divided  into  equal 
parts f  as  halves,  thirds,  fourths,  &c.,  what  are  those 
|)artj4  called  ? 

Ajis.  They  are  called  Fractions. 

2.  Q.  How  are  fractions  commonly  written? 
Ans.  By  two  numbers,  one  above  the  other,  with 

a  line  between  them.     For  example  ; 


One  half  is  written 

thus 

One  third 

M 

(( 

One  fourth 

(( 

n 

One  fifth 

u 

n 

Three  fifths 

u 

n 

One  sixth 

ii 

« 

Five  sixths 

« 

(( 

1,  <fec. 

3.  Q.  When  we  express  one  half  by  fi^gures,  t'lus 
^,  what  does  the  figure  2,  whicii  is  placed  below  the 
line,  show  ? 

Ans.  The  2  shows  that  the  number  or  thing  is 
divided  into  tvo  equal  parts; 

4.  Q.  Wha  does  the  1  placed  above  the  line,  show  ? 


FRACTIOPJS.  95 


Alls.  It  shows  that  one  of  those  parts  is  denoted 
by  the  fraction. 

5.  Q.  In  the  expression  f ,  what  dcs3  the  5,  which 
is  placed  below  the  line,  show  ? 

Ans,  It  shows  that  the  number  or  thing  is  divided 
iintojive  equal  parts. 

6.  Q.   What  does  the  3  above  the  line  show  ? 
Ans.  It  shows  that  three  of  those  parts  are  denoted 

by  the  fraction. 

7.  Q.   What  is  the  number  below  the  line  called? 
Ans.  It  is  called  the  denomlnator. 

8.  Q.  What  does  it  show  ? 

Ans.    It  shows    into   hcia   many  equal  parts   the 
number  or  thing  /*  divided. 

9.  Q.  What  is  the  number  abc'>e  the  line  called  ? 
Ans.  It  is  called  the  Numerator. 

10.  Q.   What  does  it  show  ? 

Ans.  It  shows  how  many  parts  are  expressed  by 
the  fraction. 

N.  B.  The  number  below  the  line  is  called  the  denomiria- 
tor^  because  it  gives  the  name,  as  halves,  thirds,  fifths,  &c., 
to  the  fraction.     The  number  above  the  line  is  cilled  the 
numeral  or,  because  it  numbers  the  parts,  or  shows  how  many  I 
parts  are  expressed  by  the  fraction. 

Note. — Particular  jDains  should  here  be  taken  to  explain  to  the 
young  pupil,  by  sorae  xisible  illustration,  what  the  denominator 
and  numerator  signify.     (See  Note,  p.  84.) 

j  11.  Q.  When  a  whole  number  and  a  fraction  are 
written  together,  as  "Z^,  4|,  &;c.,  what  is  the  express- 
ion called  ? 

Ans.  It  is  called  a  mixed  number. 

12.  Q.  What  then  is  a  mixed  number? 

13.  llow  are  the  expressions  2^,  and  4f,  read  ? 
Ans.  2i  is  read,  Two  and  a  half;  and  4f,  Four 

and  two  thirds. 

14     Read  the  following  :  3^;  4f  ;  Sf- ;  7| ;   lOf 


96  FRACTIONS. 


MISCELLANEOUS   EXAMPLES. 

1.  Henry  had  f  of  a  dollar,  and  his  father  gave 
him  -J-,  and  his  mother  f  of  a  dollar  more  :  how 
much  money  had  he  then  ? 

Solution. — 3  fourths  and  1  fourth  are  4  fourths, 
and  3  fourths  make  7  founhs.     Ans.   f  of  a  dollar. 

Nue. — When  the  numerator  is  e^uoi to,  or  greater  than  the  de- 
1  nominator,  the  fraction  is  called  an  improper  fraction.    Thus  f 
is  an  improper  fraction,  and  is  equal  to  if*    So  ^  is  an  improper 
fraction,  and  is  equal  to  1. 

2.  If  you  have  -^  of  a  dollar,  and  earn  |^,  and 
find  f  of  a  dollar  more,  how  much  money  will  you 
have? 

3.  A  merchant  sold  a  bushel  of  corn  for  -^  of  a 
dollar,  a  gallon  of  molasses  for  t^j  of  a  dollar,  and  a 
pound  of  tea  for  -i*^  of  a  dollar  :  how  much  did  he 
receive  for  all  ? 

4.  How  much  are  f ,  and  f ,  and  f ,  and  \  ? 

5.  How  much  are  ^,  and  -f)  ^^^^  i»  a^^d  f  ? 

6.  How  much  are  t^,  and  i^,  and  t^,  and  \^^1 

7.  If  you  have  -f  of  &  dollar,  and  lose  i  of  a  dol- 
lar, how  much  will  you  have  left  ? 

Solution. — 5  eighths  from  7  eighths  leave  2  eighths. 
Ans.  I  of  a  dollar. 

8.  If  you  have  f  of  an  orange,  and  give  away  f , 
how  much  will  you  have  left? 

9.  If  you  have  a  whole  orange  and  give  awav  « 
of  it,  how  much  will  you  have  left  ? 

10.  Take  |  from  |.  11.  Take  f  from  ^ 
12.  Take  A  from  H-        13-  ^^^^  H  ^^o^"  H- 
14.  Take  -H  from  H.        15.  Take  A  from  ij. 


FRACTIONS. 


97 


"  Scents,  how  much  wiU  ^  of  a 

16.  If  a  pear  costs  2  cents, 

near  cost  *?  u  i«  n^ar  costs  2  certs,  1  half 

1'^  irWhafwi"  V"a  barrel  of  flour  cos,  at  6 
I'lr  matTviU  i  of  a  pound  of  starch  cost,  at  9 

I  '^t  'what'cL  i  of  a  pound  of  sugar,  at  8  cents  a 
r,;^Wtcostiofapounaofhoney,at.^ 

.''r^^^dtl:tTc^^-i:a'dof.oUsses,at30 

dollars  a  hogshead  1  ^^i,^  ^  of  a  barrel 

.2-2.  At  6  doU«s  ■!  taf  of  1  ^ost  ? 

r^r/r8u:i-;ounrwhatwiiuofapoundof 

lard  cost?  i°f  \P°""tard  how  much  will  ^  of  a 

24.  At  12  cents  a  y"™'  ™     ^  ,  ^  of  a  yard  i 
I  yard  of  cambric  cost  14  of  a  yard      .^  ^.,^  ,  „f 

|y  25.  At  Ifi  cents  a  pound,  h  ^^f^pou„d? 

pound  of  ra.sms  0°^^  ?*«>»?  ^m  ^  ^  water- 

-26.  At  IB  cents  apiece,  ho^^^^^^  ^  ^^  ,  „,«r. 
melon  cost  i   -^  oi  ^ 

«^«^«^  •      . .  ^  lUr,  an  acre,  how  much  will  i  of  an 
j:;f^^*c:"rAan'acre?iofanacreM 

^  of  an  acre  ?  ^osts  30  shillings,  how 

'^'hwIlA^'awSiofaboxMotabox? 

^t.  Mfo'f'atnt'^'Vara  >>-  --'"'"'  '  '''"' 


98  FRACTIONS. 


Solution. — If  1  yard  costs  f  of  a  cent,  9  yards  will 
cost  9  times  as  much  ;  and  9  times  f  are  27  fourths, 
which  are  equal  .o  6  and  3  fourths.     .Ans,  6f  cents. 

j       30.  At  f  of  a  penny  apiece,  how  much  will  10 

'  apples  cost  ? 

31.  At  f  of  a  dollar  a  basket,  how  much  will  8 
baskets  of  peaches  cost  ? 

32.  What  will  seven  pounds  of  cinnamon  cost,  at 
i"o  of  a  dollar  a  pound  ? 

33.  What  cost  10  pounds  of  wool  at  |  of  a  dollar 
a  pound  ? 

34.  What  cost  7  pounds  of  lard,  at  8^  cents  a 
pound  ? 

Solution. — If  1  pound  costs  8^  cents,  7  pounds 
will  cost  7  times  as  much :  now  7  times  8  are  56, 
and  7  times  1  half  are  7  l»alves,  which  are  equal  to 
3  and  1  half;  and  3^  added  to  56  make  59^.  Ans, 
59i  cents. 

35.  What  cost  6  yards  of  cloth,  at  5^  dollars  per 
yard  ?  " 

36.  If  I  ride  7f  miles  an  hour,  how  far  can  I 
ride  in  7  hours  ? 

37.  A  man  bought  6  pounds  of  beef^  at  8f  cents  a 
pound:  how  much  did  he  pay  for  his  beef? 

38.  How  much  is  5  times  6f  ? 

39.  Hotv  much  is  6  times  4|  ? 

40.  How  much  is  4  times  9f  ?  i 

41.  How  much  is  8  times  6|  ? 

42.  How  much  is  7  times  lOf?  ^ 

43.  How  much  is  9  times  B^iyl 

44.  If  1  yard  of  cloth  costs  2  dollars,  how  riuch 
will  -J^  of  a  yard  cost  ? 

Sohiiion. — Since  1  yard  costs  2  dollars,  1  third 
of  a  yard  will  cost  1  third  of  2  dollars.     Now  1  tliird 


99 


' "  1  .^  o  thirds  of  1  dollar  ;  for,  1 

of  2  dollars  is  f  ^f  ^^^//  ^     d  of  2  must  be  2  tin.es 
third  of  1  is  1  linrd,  and  1  Uir  ^^^^^_ 

l^r  How  much  Willi  of  a  barrel  of  pork  cos,  at 

8  dollars  a  barrel  ?  , 

47.  What  IS  1  ha'f  "'/;;, 
Is.  What  is  1  tl-i^d  of  14  ? 

49.  What  is  1  half  of  H! 

50.  What  is!  third  of  Ih? 

51.  What  is  I  fourth  of  il? 

^%T"Vharc:'t  \  of  a  barrel  of  beer,  at  U  dollars 
^trlvhat  Willi  of  a  ton  of  hay  cost,  which. 

^'irWh:f  wilf/rJcord  of  wocKi  c»st,  at  .3 

shillings  per  cord  ?  .^^^  ;„  ^  day,  how 

57    If  a  man  can  wa^""  "", 
far  can  he  walk  in  i  o(  a  day^  ^^  ^,,„^  fo, 

59.  What  is  1  sixth  of  40  _ 

60.  What  is  1  seventh  of .«  • 

61.  What  is  1  tenth  otb.5? 

62.  Whatble..hthof74^ 

63.  What  is  1  nu-th  ol  85  . 


100  FRACTIONS. 


64.  If  1  ton  of  hay  is  worth  15  dollars,  how  much 
is  f  or"  a  ton  worth  ? 

Suggestion. — First  find  the  worth  of  |  of  a  ton, 
then  off.     Ans.  9  dollars. 

65.  If  one  acre  of  h  id  costs  24  dollars,  what  will 
"5  of  an  acre  cost  ? 

66.  What  will  f  of  h  bushel  of  corn  cost,  at  36 
cents  a  bushel  ? 

67.  What  will  -|  of  a  pound  of  tea  cost,  at  64 
cents  a  pound  ? 

68.  In  one  bushel  there  are  32  quarts :  how  nnany 
quarts  are  there  in  -^  of  a  bushel  ? 

69.  In  one  day  there  are  24  hours :  how  many 
hours  are  there  in  f  of  a  day  ? 

70.  In  one  hour  there  are  60  minutes :  how  many 
minutes  are  there  in  -^  of  an  hour  ? 

71.  A  hogshead  contains  63  gallons  :  bow  many 
gallons  are  there  in  ^  of  a  hogshead  ? 

72.  How  much  is  -f  of  27  T 

73.  Hfiy  much  is  f  of  45  ? 

74.  How  much  is  f  of  40  ? 

75.  How  much  is  f  of  54  ? 

76.  How  much  is  f  of  42  ? 

77.  How  much  is  f  of  72  '? 

78.  What  will  f  of  a  yard  of  muslin  cost,  at  35 
cents  a  yard  ? 

Analysis. — Since  1  yard  costs  35  cents,  1  fourth  of 
a  yard  will  cost  1  fourth  of  35  cents ;  and  1  fourth 
of  35  is  8  and  3  fourths.  Now,  if  1  fourth  of  a 
yard  costs  8|  cents,  3  fourths  of  a  yard  will  cost  3 
times  8J  cents;  and  3  times  8  are  24;  3  times  3 
fourtus  are  9  fourths,  equal  to  2  and  4  fourth,  which 
ad<led  to  24  mabj  26  and  1  fourth.  Therefore  J  of 
a  yard  of  mushn,  at  35  cents  a  yard,  will  coet  20J 
cents. 


\ 


FRACTIONS.  101 


79.  What  cost  f  of  an  acre  of  land,  at  20  dt  liars 
per  acre  ?  , 

80.  What  cost  f  of  a  gallon  of  molasses,  at  42 ! 
cents  per  gallon  ?  | 

81 .  Wliat  cost  f  of  a  bushel  of  pears,  at  54  cents 
a  bushel  ? 

82.  In  1  pound  there  are  20  shillings  :  Ijow  many 
shillings  are  there  in  -^  of  a  pound  ? 

88.  In  1  furlong  there  are  40  rods  :  how  many 
rods  are  there  in  f  of  a  furlong  ? 

84.  If  a  man  can  travel  40  miles  in  a  day,  how 
far  can_he  travel  in  4-  of  a  day  ? 

85.  If  a  laborer  can  earn  75  cents  in  a  day,  bow 
much  can  he  earn  in  |  of  a  day  ? 

86.  If  a  bushel  of  wheat  is  worth  87  cents.  Low 
much  is  T^  Df  a  bushel  worth  ? 

87.  How  much  is  f  of  50  ? 

88.  How  much  is  i  of  42  ? 

89.  How  much  is  |  of  56  ? 

90.  How  much  is  A  of  95  1 

91.  How  much  is  f  of  76  ? 

92.  How  much  is  i^j^  of  106  ? 

93.  A  man  sold  a  hat  for  2  dollars,  which  was 
1  half  of  what  it  cost  him :  how  much  did  he  pay  for 
the  hat  ? 

Solution. — Since  1  half  the  cost  was  2  dollars,  2 
halves  or  the  whole  cost  is  2  times  as  much  ;  and  2 
times  2  are  4.     Ans.  4  dollars. 

94.  8  is  1  half  of  what  number? 

95.  4  is  1  half  of  what  number? 

96.  7  is  1  half  of  what  number  ? 

97.  9  is  1  half  of  what  number  ? 

98.  Horace  gave  away  2  of  his  marbles,  which 


102  FRACTIONS. 

I 

was  1  third  of  all  he  had :  how  many  marbles  had 
he? 

Solution.-  -it  2  was  1  third,  3  thirds  or  the  whole 
number  must  je  3  times  2,  which  is  6.  Ans.  6 
raarbles. 

99.  4  is  1  third  of  what  number  ? 
I      100.  6  is  1  third  of  what  number? 
1      101.   10  is  1  third  of  what  number  ? 
102.  3  is  1  fourth  of  what  number? 
I      103.  4  is  1  fifth  of  what  number  ? 

104.  9  is  1  seventh  of  what  number? 

105.  A  man  bought  a  cow  and  paid  6  dollars 
down,  wliich  was  ■}■  of  the  cost :  what  was  the  price 
of  the  cow  ? 

106.  A  man  bought  a  cask  of  molasses,  and  part 
of  it  having  leaked  out,  he  found  he  had  7  gallons 
letl,  which  was  just  -J-  of  all  he  bought :  how  many 
gallons  did  he  buy  ? 

107.  If  one  man  can  do  a  piece  of  work  in  30 
days,  how  long  will  it  take  6  men  to  do  it  ? 

SuggestioH.—S  men  can  do  6  times  as  much 
work  as  1  man  ;  therefore  it  will  take  6  men  only  I 
sixth  part  as  long  as  it  will  take  1  man  :  that  is,  as 
many  days  as  6  is  contained  times  in  30  ;  and  6  is 
contained  in  30,  5  times.     Ans.  5  days. 

108.  If  a  ton  of  hay  will  last  1  horse  40  days, 
how  long  will  it  last  10  horses  ? 

109.  If  a  barrel  of  flour  will  last  1  peJ-son  63 
days,  how  long  will  it  last  a  family  of  7  persons? 

110.  If  2  yards  of  calico  cost  W  cents,  how  much 
will  .5  yards  cost  ? 

So/ution. — First  find  the  cost  of  1  yard,  then  of  5 
yards.  If  2  yards  cost  20  cents,  1  yard  will  cost 
1  half  of  20,  which  is  10  cents.     Now  if  1  yard  costs 


FRACTIONS.  103 


10  cents,  5  yards  will  cost  5  times  10  cents,  which 
are  50  cents,     Ans.  50  cents. 

111.  If  4  cl*ickens  are   worth   8  shillings,  how 
much  are  1  chickens  worth  ? 

112.  If  6  clmirs  cost  12  dollars,  how  much  will  4 
chairs  cost? 

113.  If  4  lambs  are  worth  20  shillings,  how  much 
aie  10  lambs  wcj^th? 

114.  If  5  pounds  of  butter  cost  42  cents,  what 
will  3  pounds  cost  ? 

115.  If  6  pounds  of  cheese  cost  32  cents,  what 
will  4  pounds  cost  ? 

116.  If  4  yards  of  calico  cost  37  cents,  what  will 
10  yards  cost  ? 

117.  If  4  boys  can  saw  a  cord  of  wood  in  3  hours, 
how  long  will  it  take  6  boys  to  saw  a  cord  ? 

118.  If  6   teams  can  plough  a  field  in  8  howrs, 
how  long  will  it  take  8  teams  to  plough  it  ? 

119.  If  10  men  can  doti  job  of  work  in  6  days, 
how  long  will  it  take  '  2  men  to  do  it  ?  " 

120.  If  J  a  yard  of  cloth  costs  6  dollars,  what 
will  1 0  yards  cost  ? 

121.  If  I  of  3  barrel  of  flour  costs  12  shillings, 
what  will  9  barrels  cost  ? 

122.  If  f  of  a  ton  of  hay  costs  9  dollars,  What 
will  6  tons  cost  ? 

123.  If  9  yards  of  ribbon  cost  72  cents,  what  wiil 
i  of  a  yard  cost  ? 

12  4.  If  12  bushels  of  salt  cost  48  shillings,  what 
will  f  of  a  bushel  cost  ? 

125.  If  i  of  a  firkin  of  butter  costs  4  dollars,  what 
will  I  of  a  firkin  cost  ? 

126.  If  I  of  an  acre  of  land  costs  19  dollars,  how 
much  will  f  of  an  acre  cost  ?  I 


UBLtS  OP  MONEY,  WEIGHTS,  AND  MK^SUKES. 

FEDERAL  MONEY. 

I.  Federal  Money  is  the  TJurrency  of  the  United 
States.  The  denominations  are,  Eagles,  dollars, 
dimes,  cents  and  mills. 

10  mills  (m.)  make  1  cent,  marked  ct. 

10  cents  "      1  dime,      "  d. 

10  dimes  "      1  dollar,     "  doU.  or  $. 

10  dollars  "      1  eagle.      "  E. 

II.  The  national  coins  of  the  United  States  are 
of  three  kinds,  viz :  gold,  silver,  and  copper. 

1.  The  gold  coins  are  the  eagle,  half  eagle,  and 
quarter  eagle,  tlie  double  eagle,  and  gold  dollar, 

2.  The  silver  coins  are  the  dollar,  Jialf  dollar, 
quarter  dollar^  the  dime^  half  dime,  and  three-cent-piece. 

3.  The  copper  coins  are  the  cent  and  half  cent. 
Mills  are  not  coined. 

Note. — Federal  money  was  established  by  Congress,  August  i 
8th,  1786.  Previous  to  this,  English  or  Sterling  money  was  j 
the  principal  currency  of  the  country. 

STERLING  MONEY.  | 

1£I.  Sterling  or  English  Money,  is  the  national  I 
currency  of  Great  Britrtin.  I 

4  farthings  {qr.  or  far.)  make  1  penny,  marked    d, 

12  pence  "      1  shilling,  "  s. 

20  shillings  "      1  pound,  or  savereign,    j6. 

*il  shillings  "      1  guinea. 

ar«8T.— 1.  What  is  Federal  Money?  Recite  the  Table.  2  Of  how 
many  kinds  are  the  coins  of  the  United  States  ?  What  are  the  gold 
coins  ?  What  are  the  silver  coins  ?  The  copper  coins  1  When  and 
by  whom  was  Federal  Money  esiiiblished  1  3.  What  U  Sterling  Mon- 
ey 1  R«peat  the  TaWe.  n<m  many  farihintrs  iii  2  j>eace  7  in  :<[*«»<■*  ^ 
In  5  pence  Jtc  ?  How  many  pence  in  2  shillings  T  In  4  shii'iniiB,  «.' .  > 
In  S  farthings  how  many  ^.ence  T    In  \1  far  T     lu  14  far  1 

^ft}t«  — -Uuestiooa  like  the  precedinf  n.ay  be  a^sked,  with  adva&tage, 
opon  eAch  of  the  subsequent  'I'ableB. 


WEIGHTS    AND    MEASURES.  10*6 

Obs.  The  Pound  Sterling  is  represented  by  a  gold  coia, 
called  a  Sftver^'mn.  Its  IcfiaL  value,  according  to  ArA  of  Cmi- 
:^resi,  IS452,  is  S4.84  ;  its  in{rm$ic  value,  according  to  assays 
at  the  U.  S.  mint,  is  S4.86i.  The  legal  value  of  an  Engiiah 
shilling  ia  '24^  cents. 

TROY   WEIGHT. 

IV.  Troy  Weight  is  used  in  weighing  gold,  sil- 
ver, jewels,  liquors,  tfec,  and  is  generally  adopt(?d  in 
philosophical  experiments. 

24  grains  {i(r.)         make  1  pennyweight,  markud  jnt^t, 
20  pennyweights        "      1  ounce,  "         oz. 

12  ounces  "      1  pound,  "  lb. 

Note. — Most  children  have  very  erroneous  or  indistinct  ideas 
of  the  weiirhts  and  measures  in  common  use.  It  is,  therefore, 
strongly  recommended  for  teachers  to  illustrate  them  practi- 
cally, by  referring  to  some  visible  object  of  equal  magnitude, 
or  by  exhibiting  the  ounce,  the  pound ;  the  linear  inch,  foot, 
yard,  and  rod ;  also  a  sqitare  and  cubic  inch,  foot,  Slc. 

AVOIRDUPOIS  WEIGHT. 

V.  Avoirdupois  Weight  is  used  in  weighing  gro- 
ceries and  all  coarse  articles  ;  as  sugar,  tea,  coffee, 
butter,  cheese,  liour,  hay,  «fec.,  and  all  metals  except 
gold  and  silver. 

If)  drams  (<^.)  make  1  ounce,    marked      oz. 

16  ounces  "       1  pound,        "  lb. 

I  25  pounds  j         "1  quarter,       "  qr. 

I  4  quarters,  or  lot*  lbs.  "       I  hundred  weight,    cwl. 

j  *20  hnn.!..  or 'XK'O  Hw      "       1  t„n,   marked  T 

\  0b8.  1.  CrToai  weight  is  the  weight  of  good.9  with  the  boxes, 
,  casks,  or  bags,  which  contain  them,  and  allows  112  lbs.  for  a 
'  hundred  weight. 

j      Net  weight  is  the  weight  of  the  goods  only. 
i      2    Formerly  it  was  customary  to  allow  112  poands  for  a  hun- 
i  dred  weight ;  but  the  laws  of  most  of  the  states,  as  well  as  gene- 
'  ral  usage,  now  call  100  lbs.  a  hundred  weight. 

j  Qn^T.— 0*«.  By  what  i.-s  tho  Pound  Sterling  represented V  \^  l>r.t  *f 
its  lesral  v»<lue  in  dofars  and  ccula  1  What  is  the  valua  of  an  Biuillsii 
ehilliiiv??  4.  In  what  is  Tn.y  Weiuht  used?  Recite  the  Table.  5.  In 
what  ia  Avolrdur)oiB  Weiglit  ubo«1  1  Recite  the  Table.  Ob$.  What  is 
irross  weip'bl  1     What  is  not  weiglitY     How  many  pi>u"ilR  were  formerly 

■  nl !•>*«.(  l-r  n  htuilred  weight '? 


106  WEIGHTS    AND    MEASURES. 


APOTHECARIES'  WEIGHT. 

VI.  Apotliecaries'  Weight  is  used  by  apothec&« 
ries  and  physicians  in  mixing  medicines. 

20  grains  (gr.)  make  1  scruple,  meOrked    sc.  or  3 . 

3  scruples  «'      I  dram,  "         dr.  or  3 . 

8  drams  "      I  ounce,         "        oz.  or  I . 

12  ounces  "      1  pound,         V,  ft. 

Obs.  1.  The  pound  and  ounce  in  tliis  weight  are  the  same 

as  the  TVv)t/  pound  and  ounce;  the  sicddnnsums  of  the  O'unce 

are  different. 

2.  Drugs  and  medicines  are  bought  and  sold  by  avoir dup&is 
weight. 

LONG  MEASURE. 

VII.  Long  Meaaure  is  used  in  measuring  length  or 
distances  only,  without  regard  to  breadth  or  depth. 

12  inches  {in.)  make  1  foot,            marked      ft. 

3  feet  "      1  yard,               "          yd. 

5^  yards,  or  16j  feet  "      1  rod.  perch,  or  pole,  r.orj>. 

40  rods  "      1  furlong,     marked   fur. 

8  furlongs,  or  320  rods  "      1  mile.                *'           w. 

3  miJes  "^   1  league,            "             I. 

3H0  dcii.  make  a  great  circle,  or  the  circumference  of  the  earth 

Obs.  1.  4  inches  make  1  hand  ;  9  inches,  1  span;  18  inche*, 
1  cubit ;  6  feet,  1  fathom  ;  4  rods  or  100  links,  1  chain ;  25  links, 
1  red ;  7tVo  inches  1  link, 

2.  Long  measure  is  frequently  called  litiear  or  lineal  meas- 
ure.    Formerly  the  inch  was  divided  into  3  barleycorns ;  bul  • 
the*  barleycorn!  as  a  measure,  has  become  obsfiletc.     The  inch  j 
is  commonly  divided  either  into  eighths  or  ten'-hs;  sometimes, 
it  is  divideti  into  fioelfths,  which  are  called  linus. 

attEBT.— T).  [n  what  is  Ajiothecaries'  Weight  used  ?  Tepeat  the 
Table.  To  what  are  the  apothecaries'  pound  and  ounce  eqi  al  1  How 
are  drugs  and  medicines  bought  and  sold  ?  7.  In  what  is  Long  Meas- 
ure used  J  Repeat  the  'I'uble  Draw  a  hne  an  inch  lone  up< «  your 
slate  or  b  acit-hoard.  I»ravv  one  two  inches  long.  Draw  another  a  foot 
long.  J -raw  one  a  yard  long.  n«w  long  is  your  teacher's  desk  ?  llnw  ! 
Ions  is  the  schoolroom  1  How  wide  ?  Obs.  W  hat  is  long  laeasure  fre-  ! 
qnently  called  1   How  la  the  inch  comnioniy  divided  at  the  present  day  7   | 


WEIGHTS    AND    MEASURES. 


107 


CLOTH  MEASURE. 

VIII.  Cloth  Measure  is  used  in  measuring  cloth, 
lace,  and  all  kinds  of  goods  which  are  bought  or 
sold  by  the  yard. 

'2\  inches  (m.)    make  1  nail,  marked  tm. 

4  nails,  or  9  in       "      1  quarter  of  a  yard,     *'        qr, 

4  quarters  "      1  yard,  "        yd. 

3  quarters  "      1  Flemish  ell,  "    Fl.  e. 

5  quarters  "      1  English  ell,  "     E.e. 

6  quarters  "      1  French  ell,  "     F.  e. 
Obs.  Cloth  measure  i?  a  species  of  hnig  measure.     The  yard 

is  the  same  in  both.     Cloths,  laces,  &c.,  are  Iwught  and  sold 
by  the  linear  yard,  without  regard  to  their  width. 

SQUARE  MEASURE. 

IX.  Square  Measure  is  used  in  measuring  sur- 
faces, or  things  whose  length  and  breadth  are  con- 
sidered without  regard  to  heighth  or  depth  ;  as  land, 
flooring,  plastering,  &c. 

144  square  in.  (s//.  in.)    make  1  square  foot,  marked  5r/.  ft. 

9  square  feet  "      1  square  yard,  "      sq.yd 

20\  square  yards,  or  )        ,,  (  1  sq.  rod,  perch,  ^^ 

'2Ti\  square  feet  \  (or  pole, 

40  square  rods  "      1  rood,  " 

4  rootls,  or  160  sq.  rods    "      1  acre,  " 
"      1  square  mile,  *' 


640  acres 

Obs  1.  A  square  is  a  figure  which 
has  faur  equal  sides,  and  all  its  angles 
ri'^ht-aniilcs,  as  seen  in  the  adjoining 
figure.     Hence, 

"2.  A  Square  Inch  is  a  square,  whose 
•ides  are  each  a  linear  inch  in  length. 

3.  A  Squav.  Fon/  is  a  square,  whose 
hides  are  each  a  linear  foot  in  length. 

4.  A  Square  V^ri-/ is  a  square,  whose 
sides  arc  each  a  linear  yard  or  three 
linear  feet  in  lentrth,  and  contains  9 
square  feet,  as  reprcsenteil  by  the  adjacent  figure. 

CirKST.— 8.  In  whfit  is  Cloth    Measure  used  1      Repeat  the  Table 
9.  1.1  what  is  Square  Measure  u.^ed  1     Repeat  the  Table. 


108  WKIGHTS    AND    MEASURES 

CUBIC  MEASURE. 

X.  Cubic  Measure  is  used  in  measuring  solid 
bodies,  or  things  which  have  length,  breadth,  and 
thickness,  such  as  timber,  stone,  boxes  of  goods,  the 
capacity  of  rooms,  <fec. 

1728  cubic  inches  (ctt.iu.)  make  1  cubic  foot,      marked  cu.  ft 
'27  cubic  feet  "      I  cubic  yard,  "      cu.  yd 


40  feet  of  round,  or 
50  ft.  of  hewn  timber 


1  ton  «  T. 


42  cubic  feet  "       I  ton  of  shipping,  "  T. 

16  cubic  foe.  "VZi:Z'Z^\"        c.fi. 


8  cord  feet,  or 
128  cubic  feet 


I  cord,  "  C. 


Obs.  1.   A  pile  of  wood  8  feel  lon^,  4  feet  wide,  and  4  feet 
high,  contains  1  cord.     For  8  into  4  into  4=128. 
2.  A  CvJba  is  a  solid  body  bound-  y     y      ^ 


/ 


j  e«l  by  s.ix  equal  squares.     It  is  often       y^      /     y^ 

j  called  a  kexaedron      Hence, 

j       A   Cvbic  Itich  is  a  cube,  each  of 

I  whose  sides  is  a  sqiuirr.  inch,  as  rep- 

I  resented  by  the  adjoining  figure. 

'       A  Cubic  Foot  is  a  cube,  each  of 

i  whose  sides  is  a  square  foot. 

j       3.  The  Cubic  l^m  is  chiefly  used 
in  estimating  the  cartage  and  trans-    1=-  _1- 

i  portation  of  timber.     By  a  tmi  of  round  tiiiibei  is  meant,  such 

!  a  quantity  of  timber  in  its  rough  or  natural  state,  a*'  when 

I  hewn,  will  make  40  cubic  feet,  and  is  tiup[»o8ed  t.o  l»e  equal  ib 

I  weight  to  50  feet  of  hewn  timber. 

!       4.  The  cvbic  Um  or  had,  is  by  no  means  an  o/xurate  or  unu- 

\  form  standard  of  estimating  weight;  for,  different  kinds  of 
timbtr,  are  of  very  different  degrees  of  density.  But  it  is  per- 
haps sufficiently  accurate  for  the  pur]»ose8  to  which  it  is  ap- 

j  plied. 

i  Upest. — Ohs.  What  Is  a  square  ?  What  Is  a  squsjr  itch  ?  What 
I  is  a  square  foox  ?    A  square  yard  1   Can  you  draw  a  square  Inch  ?    Can 

you  draw  «  sqiiare  foot  ?  A  square  yard  *?  10  In  what  is  C\>bic  Mea*- 
I  lire  used  1  Recite  the  Table.  How  long,  wide,  and  hifh,  ninst  a  pile 
!   of  wood  be  to  makf  a  r.<»r(  1     What  is  a  cube  ?     What  is  a  cable  inch  1 

'^'hai  )-  u  ci-itic  f'tot "?    Can  you  draw  a  <'u><c  inch  on  your  slate  1 


WEIGHTS    AND    MEASUKBS.  109 

WINE  MEASURE. 

XI.  Wine  Measure  is  used  in  measuring  wine, 
I  aloohol,  molasses,  oil,  and  all  other  liquids  except 
;  beer,  ale,  and  milk. 

4  gills  (gi.)  make  1  pint,          marked  pi. 

2  pintg."  '*      1  quart.             «*  qt 

4  quarts  "      1  gallon,            "  gal 

Sl^gaPiOns  *»      1  barrel,            "      bar.otbbl 

4'2  gaFions  "      1  tierce,             "  tier 

63  gallons,  or  2  bbis,   "      1  hogshead,      "  hAd 

2  hogsheads  "      1  pipe  or  butt,   "  pi 

2  pipes  "      1  tun,                "  tun 

Obs.  The  wine  gallon  contains  931  cubic  inches. 

BEER  MEASURE. 

XII.  Beer  Measure  is  used  in  measuring    beer, 
ale,  and  milk. 

2  pints  (pts.)        make  1  quart,         marked  qt. 

4  quarts  **      1  gallon,  "  gai. 

36  gallons  "      1  barrel,  "     bar.  or  bbl. 

54  gals,  or  IJ  bbls.    "      1  hogshead,        '«  hhd. 

Obs,  The  beer  gallon  contains  282  cubic  inches.     In  many 

places  milk  is  measured  by  wine  measure. 

DRY  MEASURE. 

XIII.  Dry  Measure  is  used  in  measuring  gn\\n 
•ruit,  salt.  &c. 

2  pints  {pts.)  make  1  quart,  marked      qt. 

8  quarts  "      1  peck,  "  pk. 

4  pecks,  or  32  qts.       "      1  bushel,  "  ^t, 

8  bushels  '•      I  quarter,  "  qr. 

32  bushels  **      1  chaldror,  "  ck. 

Note. — In  England,  36  bushels  of  coal  nake  a  chaldron. 

QrK«T. — II.  In  what  Is  Wine  Measure  used?  Recite  the  Tahln. 
Obif.  Mow  many  cubic  inches  in  a  wine  gallon?  12.  In  what  Is  Beer 
Measiire  used  T  Repeat  the  Tai>ie.  Obs.  How  many  cubic  inches  In  a 
beer  gallon  ?    13.  In  what  is  ii/y  Measure  used  ?     Recite  the  Table. 


"■"i-«VU-  -jppw 


Mil 

110 


make  1  minute, 

marked  min 

"     1  hour, 

'«      hr. 

"     1  day, 

"      d. 

"     1  week. 

'•      wk. 

"     1  lunar  month, 

"      mo. 

"     1  civil  year, 

«•      yr. 

TIME. 

XIV.  Time  is  naturally  divided  into  days  end 
years  ;  tiie  former  are  caused  by  the  revolution  of  the 
Earth  on  ite  axis,  the  latter  by  its  revolution  round  the 

Sun. 

60  seconds  {see.) 
60  minutes 
24  hours 

7  days 

1  weeks 

12  calendar  months,  or     / 
365  days,  6  hrs.,  (nearly,)  ) 

13  lunar  months,  1  day,  and  6  hours  (nearly),  make  1  year. 

Obs.  1.  Time  is  measured  by  clocks,  watches,  chronometers, 
dials,  hour-glasses,  Ac. 

2.  A  civil  year  is  a  legal  or  common  year  ,  a  period  of  time  es- 
tablished by  government  for  civil  or  common  purposes. 

3.  A  solar  year  is  the  exact  time  in  which  the  earth  revolves 
round  the  sun,  and  contains  365  days,  5  hrs.  48  min.,  and  48  sec. 

4.  A  Bissextile,  or  Leap  year,  is  a  year  which  contaixis  366 
days,  and  occurs  once  in, /our  years. 

It  is  caused  by  the  excosa  of  6  hours,  which  the  civil  year  con- 
tains above  365  days,  and  is  so  called  because  it  leaps  or  runs 
over  one  day  more  than  a  common  year. 

The  odd  day  is  added  to  February,  because  it  is  the  shortest 
month.     Every  leap  year,  therefore,  February  has  29  days. 

XV.  The  names  of  the  days  of  the  week  are  the 
following :  Sunday,  (first  day,)  Monday,  (csecond,) 
Tuesday,  (third,)  Wednesday,  (fourth,)  Thursday, 
(fifth,)  Friday,  (sixth,)  Saturday,  (seventh.) 

Obs.  The  names  of  the  days  of  the  week  are  derived  from  the 
names  of  certain  Saxon  deities  or  objects  of  worship.     Thus, 

Sunday  is  named  from  the  sun,  because  this  day  was  dedicated  ! 
to  its  worship.  I 


Q,CK8T. — 14.  Hi3w  is  Time  naturally  divided  ?    How  are  tJ^o  \>nnor  i 
caused  1    How  the  latter  7    Repeat  the  Tabic.    Obs.  How  is  Tim<  meas- 
ured ?    What  is  a  civil  year  1     A  solar  >  ear  ?    A  leap  year  ? 


Ill 


Mond^iy  «  named  from  the  moon,  to  whose  worship  it  was 
dedicated. 

"^rvesdny  is  ikrived  from  'Piiisco,  the  Saxon  god  of  war. 

Wediiestluy  i»  derived  from  Woden,  a  deity  of  northern 
Euroj>e. 

T/mrsday  if  from  T/w/r,  the  Danish  god  of  thunder, 
storms,  &c. 

Friday  is  from  Fri^a,  the  Saxon  godiless  of  beauty. 

Saturday  is  from  the  planet  Saturn,  to  which  it  wae  dedicated. 


XVI.  The 

following  are  the  names  of  the 

12  cal- 

endar  months  into  which  the 

civil 

year 

is  divided ; 

with  the  number  of  days  in  each  : 

January, 

(Jan.) 

{Feb.^ 

Mar.) 

(Apr.) 

Jirst      month, 

has 

31 

dajs. 

F"ebruary, 

■second 

t( 

(1 

28 

(1 

March, 

third 

(1 

(( 

31 

(1 

April, 

fourth 

3e 

(i 

May, 

(May) 

M'^ 

31 

(( 

June, 

(June) 
(July) 

sixth 

30 

« 

July, 

seventh 

31 

<i 

August, 

(Aug.) 

ei^Uh 

31 

« 

September, 

rScpt.) 

ninth 

3t 

(( 

October, 

(Oct.) 

tenth 

3! 

« 

November, 

(Nov.) 

eleventh 

3(1 

« 

December, 

(Dec.) 

twelfth 

3i 

t( 

Obs.  The  number  of  days  in  each  month  may  b«  •^idy  re- 
membered from  the  following  lines : 

"  Thirty  days  hath  September, 
April.  June,  and  November; 
February,  twenty-eight  alone, 
All  the  rest  have  thirty-one; 
Except  in  Leap  Year,  then  is  the  time, 
When  February  has  twenty-nine." 

Obs.  Tlie  names  of  the  calendar  months  were  borrowed  from 
the  Kouiaus,  and  most  of  them  liad  a  fanciful  orijrin.    Thus, 

January,  was  nsimed  after  Janu^,  a  Roman  deity,  who  was 
supposed  to  preside  over  the  year  and  the  conimencemeiit  of  all 
undertakings. 

February,  was  derived  from  feoruo,  a  Latin  word  which  siarni- 
fies  to  purify  by  sacrifice^  and  was  so  called  because  this  month 
was  devoted  to  the  purihcation  of  the  people. 


March  was  named  after  Mara,  the  Roman  god  of  war  ;  and 
was  originally  the  first  month  of  the  Roman  year. 

April,  from  the  Latin  aperio,  to  open,  was  so  called  from  ths 
opening  of  buds,  blossoms,  Ac,  at  this  season. 

May  was  named  after  the  goddess  Maia,  the  mother  of  Mer- 
cury, to  whom  the  ancients  used  to  offer  sacrifices  on  the_^rfi/  day 
of  this  month. 

1     June  was  named  after  the  goddess  Juno,  the  wife  of  Jupiter. 
July  was  so  called  in  honor  of  Julius  Ccesar,  who  was  born  in 
this  month. 

i     August  waa  so  called  in  honor  of  Augustus  Caesar,  a  Roman 
I  Emperor,  who  entered  upon  his  first  consulate  in  this  month. 

SeptcTuber,  from  the  Latin  numeral   sepfem,  seven,  was  so 
I  called,  because  it  wa*  originally  the  seventh  month  of  the  Roman 
year.     It  is  the  ninth  month  in  our  year. 

I      October,  from  the  Latin  octo,  eight,  was  so  called  because  it 
I  was  the  eighth  month  of  the  Roman  year. 

j      November,  i  -om  the  Latin  novem,  nine,  was  so  called  because 
■  it  was  the  ninth  month  of  the  Roman  year. 
I      December,  from  the  Latin  decern,  ten,  was  so  called  because  it 
was  the  tenth  month  of  the  Roman  year. 

XVII.  Tue  year  is  also  divided  into  /our  seasons, 
of  three  months  each,  viz :  Spring,  Summer,  Autumn 
or  Fall,  and  Winter. 

Spring  comprises  March,  April,  and  May ; 
Summer,  June,  July,  and  Aus^ust ; 
Autumn  or  Fall,  September,  October,  and  November; 
Winter,  December,  January,  and  Februaiy. 

CIRCULAR  MEASURE. 

XVIII.  Circular  Measure  is  applied  to  the  divisions 
of  the  circle,  and  is  used  in  reckoning  latitude  and  lon- 
gitude, and  the  motion  of  the  heavenly  bodies. 

60  seconds  (")  make  1  minute,  marked  '. 

60  minutes  "     1  degree,         "      °. 

30  degrees  "     1  sign,             "      ». 

12  signs,  or  360°  "     1  circle,           "      c. 


Que  ST.— 17.  Name  the  seasons.    18.  To  what  is  Circular  Measure  ap- 
plied ?    Repeat  the  Table. 


"^^^^^^HTS    AND    MEASURES. 


o    The  circumference  of 
every   circle  is  ^^'^'^f '.  ^^ 

3G0  equal  parts,  calleV^- 
;  ^rce5,  as  in  the   subjoined  ^ 

'  figuf^-  .       I     1 

3    Since  a  degree  is  ^  6^ 

part  of  the  circumference  of 
I  a  circle,  it  is  obvious  that  U8 

length  must  depend  on  the 

siie  of  the  circle. 

MISCELLANEOUS  TABLE. 


12  units 

1-2  dozen,  or  144 

1-2  gross,  or  1T2» 

20  units 
56  pounds 

100  pounds 

196  pounds 

•200  pounds  ^,  ip„d 

14  pounds  01  iron,  or  lead 

21  i  stone 
Spigs 


make  I  dozen,  id4>z.) 
1  gross. 
1  great  gro8». 
I  score. 

I  arkin  of  butter. 
1  quintal  of  fi-^h. 
Ibar.offishmMaae^ 
Ibar.  inN.Y.  andCt. 

I  bar.  of  flour. 

I  bar.  of  pork. 

1  gtone. 


I  fothcr. 


114  STATE    CURRENCIKS. 

PAPER  AND  BOOKS. 

X\.  The  terms,  folio,  quarto,  octavo,  <fec.,  applied 
to  books,  denote  the  number  of  leaves  into  which  a 
sheet  of  paper  is  folded. 


24  sheets  of  paper 

make 

1  quire. 

20  quires 

(( 

1  ream. 

2  reams 

(( 

1  bundle 

5  bundles 

« 

1  bale. 

A  sheet  folded  in  two  leaves,  is  called  a  folw. 
A  sheet  fohled  in  four  leaves,  is  caJIed  a  quarto^  or  4/o. 
A  sheet  folded  in  eight  leaves,  is  called  an  octavo^  or  8tJo. 
A  .:*ieet  folded  in  twelve  leaves,  is  called  a  dtuidecinw. 
A  sheet  folded  in  sixteen  leaves,  is  called  a  \^mo. 
A  sheet  folded  in  eighteen  leaves,  is  called  an  I8md. 
A  sheet  folded  in  thirty-two  leaves,  is  culled  a  'i-2mn. 
A  sheet  folded  in  thirty-six  leaves,  is  called  a  'ifjvw. 
A  sheet  folded  in  forty-eight  leaves,  is  called  a  48wm>. 

XXI.  Previous  to  the  adoption  of  Federal  money 
in  1786,  accounts  in  the  United  States  were  kept  in 
pounds,  shillings,  pence,  and  farthings. 

In  New  England  currency,  Virginia,  ) 

Kentucky,  Tennessee,  Indiana,  II- >  6  shil.  make  SL 

linois,  Missouri,  and  Mississippi,        ) 
In  New  York  currency,  North  Caro-  j  g  ^^      ^ 

Una,  Ohio,  and  Michigan,  j  •««»«>  « 

In   Pennsylvania  currency,  New  Jer-  )  -    /. ,         .     jm 

scy,  Delaware,  and  Maryland,  \  ^*'  ^'  "^^^^  ^^• 

In  Georgia  currency,  and  South  Car-  ^  j -  uj  __u    »• 

In  Canada  currency,  and  Nova  Scotia,     5  shil.  sake  $1. 

Obs.  At  the  time   Federal  money  was  adopted,  the  colwiial 
i  CKrreTicy  or  bills  of  credit  issued  by  the  colonies,  had  more  or 


Q.UK8T. — 20.  When  a  sheet  of  paper  is  folded  into  two  leaves,  what 
is  it  called  1  When  into  four  leaves,  what  7  When  into  eight?  Into 
twelve  1  Into  sixteen  1  Into  eij?ht«'en  1  Into  thirty  six "?  21.  Previoo* 
to  the  adoption  of  Fedeml  Money,  in  what  wei<  accounts  ke^t  in  ih« 
U.  8.  ■»  How  many  shillings  malce  a  dollar  in  N.  E.  currency  1  In  N  Y. 
currency  7    la  Penn.  currency  1    In  Georgia  car.  1    In  Caniid&  cur.  1 


ALIQUOT   PAETS.  115 


less  depreciated  in  value:    that   is,  a  colonial  pound  was  worth 
less    than    a    pound    Sterling;    a    colonial    shillinsr,    than     a    shil- 
ling   Sterling,    &c.      This     depreciation    being     greater    in     some 
colonies  than  in  others,  gave  rise  to  the  difer(dnt    values  of  the    | 
/State  currenciea. 


ALIQUOT   PAETS   OF   $1    IN   FEDEBAL   MONEY. 


60  cents  =  %\ 
831-  cents  =  $i 
25  cents  =  $i 
20  cents  =  $1- 
16f  cents  =  %l 


12^  cents  =  $g- 

10  cents  =  $,\f 

8i  cents  =  %^ 

6i-  cents  =  $i 

5  cents  =  $7 

2'U 


« 

PARTS    OF    $1    IN    NEW    YORK    CURRKNCV. 


4  shillings  =$i 

2  shil  8  pence     —^\ 
2  shillings  ~^\ 


1   shilling  4  pence  =  $1 
1   shilling  =$i 

6  pence  =^tV 


Obs.  1.  In  New  York  currency,  it  will  Se  seen,  (Art.  21,)  that 
A  8ix-i>ence,  written      M.   =     6}  cents. 

A  shilling,  "  l«.  =   l-2i      » 

One  (shil.)  and  6  pence        "  1/G.  =   \hi      " 

Two  ehillings,  "  2s.  =  25        " 


PARTS    OF    $1    IN    NKW    ENGLAND    CURRENCY. 

1  shilling  = 

9  pence  = 


3  shillings  =8^ 

2  shillings  =Si 

1   shil.  and  6fl.      =$i 


6  pence  =$t^ 


Oba.  2,  In  New  En^^land  currency,  it  will  be  seen,  that 

A  four-y>ence-half-[)cnny,  written  4id.  =     6^  cents. 

A  flix-pence,                             "  6d.  =     8^      «« 

A  nine-pence,                          "  i*d.  =   12^      " 

A  sKdhnj;,                                "  Is.  =   ir)|      " 

One  (ahil.)  and  six- pence     "  1/6.  =  25        '' 

Two  8hiIUng«,                        "  2s.  =  33^      " 

QuBST.— What  are  the  aliquot  parts  of  $1  in  Federal  Money  1  In 
New  Yiirk  currency?  In  New  England  currency  ]  What  are  the  ali- 
quot parts  of  a  i>ound  Sterling  1    Of  a  shilling  "? 


116                                     ALIQUOT   PARTS.                                             | 

ALIQUOT    PARTS    OF 

STERLINa    MONET.                     | 

Parts  ef  £\. 

Paris  of  Is. 

10  shil.    =  £\ 

6    pence  —^    shil 

6s.  8d.  =^  £\ 

4    pence  =i    shil. 

5  shil.    =  £} 

3    pence  =i    shil.         i 

4  shil.    =  £i 

2    pence  =f    shil.         | 

'            3s.  4d.  =  £| 

1^  pence  =\    shil.         1 

^            2s.  6d.  =   JCi 

1    penny =^4  shil. 

i            2  shil.    =  £tV 

1    far.=-J-  penny. 

Is.  8d.  =  £t^ 

2    far.=i^  penny. 

1  shil.    =  £^ 

3    far.=f  penny. 

ALIQUOT    PARI 

'8    OF    A    TON.  - 

10  hund.  Ibs.=i  ton. 

2  hund.  2  qrs.  =  i  ton.      | 

6  hund.  lbs.=-}-  ton. 

2  hund.  lbs.    =t^  ton. 

4  hund.  lbs.=i  ton. 

1  hund.  lbs.    =t^  ton.    ' 

ALIQUOT    PARTS    OF    A 

POUND    AVOIRDUPOIS.              j 

8  ounces=^  pound. 

2  ounces =i  pound. 

4  ounces =-}^  pound. 

1  ounce  =tV  pound.      j 

ALIQUOT   PAl 

ITS    OF   TIME. 

Parts  of  1  year. 

Part^  of  1  month. 

6     months = -J-  year. 

15  days=i     month. 

4     months =■}  year. 

10  days=-i^     month. 

'      3     months =1  year. 

6  days=j     month.      { 

2     months = -J-  year. 

6  days=3J     month       ' 

1  \  month  =  1  year. 

3  days=T^  month,      i 

ij  month  =1  year. 

2  days  =  T*j  month. 

1     month  =T^  year. 

1  day  =f^  mcnth.      j 

EXERCISES  IN  COMPOUND  NUMBERS. 

1.  In  4  cents,  how  many  mills?     In  6  cents? 

2.  In  5  dimes,  how  many  cents  ?     In  7  dimes  ? 

3.  In  $2,  how  many  cents  ?     In  $3  ?     In  84  ? 

4.  How  many  dollars  in  5  eagles  ?     In  6  E.  ? 

5.  How  many  eagles  m  *40  ?    In  $55  ?    In  |!67  ? 

6.  How  many  dollars  in  60  dimes  ?    In  76  dimes  ? 

7.  How  many  mills  in  ^  cent  ?     In  ^  cent  ?     In 
i  ct.  ?     In  I  ct.  ? 

8.  How  many  cents  in  ^  dollar  ?      In  ^  doll.  ? 
In  I  doll.  ? 

9.  In  4  pence,  how  many  farthings?     In  6  d.  ? 

10.  In  2  shillings,  how  many  pence?     In  4  s.  ? 

11.  In  2  pounds,  how  many  shillings?     In  £4? 

12.  In  5  farthings,  how  many  pence?     In  6  far.  ? 

13.  How  many  shillings  in  18  ponce  ?     In  24  d.  ? 

14.  How  many  pounds  in  40  shiUings  ?     In  60  s.  ? 

15.  How  many  farthings  in  i  penny  ?     In  -J^  d.  ? 
In  i  d.  ?     In  H  d.  ?     In  2i  d.  ?     In  4^  d.  ? 

16.  How  many  pence  in  t^  shilling?     In  -J  s.  ? 
In  is.?     In  is.?     In  Is.?    In  H  s.  ?     In  2i  s.  ? 

17.  How  many  shillings  in  -^  pound?     In  £|  ? 
In  £i  ?     In  X|  ?     In  £f  ?     In  £H  ?     In  £2j  ? 

I       18.   How  many  ounces  in  2  lbs.,  Troy  weight? 

I  Ixx  3  lbs.  ?     In  4  lbs.  ? 

I       19.  How  many  ounces  in  ^  lb.,  Troy  ?     In  -J  lb.  ? 

1  In  i  lb.  ?     In  i  lb.  ?     In  li  lb.  ?     In  2i  lbs.  ? 

I       20.  How  many  pwts.  in  -J-  oz.,  Troy  ?     In  -J-  oz.  ? 

j  Inioz.?     In  I  oz.? 

!      21.  How  many  grains  in  j[  pwt.  ?     In  ^  pwt.  ? 

I  In  -f  pwt.  ?     In  I  pwt.  ? 

!       22.  In  2  tons,  how  many  hundred  weight  ?     In  3 

1  tons  ?     In  4  tons  ? 


118  COMPOUND 


23.  In  ^  lb.  Avoir.,  how  many  ounces  ?»  In  ^  lb.  ? 
In  I  lb.  ?     In  H  lb.  ?     In  2i  lbs.  ? 

24.  In  ^  oz.,  Avoir.,  how  many  drams  ?     In  }  oz  ? 

25.  In  i  ton,  Avoir.,  how  many  cwt.  ?  In  -J-  ton  ? 
In  ^  ton  ? 

26.  In  2  feet,  how  many  inches  ?     In  4  ft.  ? 

27.  In  2  yards,  how  many  feet  ?  In  3  yds.  ?  In 
4  yds.  ?     In  5  yds.  ?     In  10  yds.  ? 

28.  In  2  rods,  how  many  yards  ?  In  3  rods  ?  In 
4  rods  ?     In  5  rods  ? 

29.  In  2  furlongs,  how  many  rods  ?    In  3  furlongs  ? 

30.  In  2  miles,  how  many  furlongs  ?  In  3  miles  ? 
In  4  miles  ? 

31.  In  3  leagues,  how  many  miles  ?     In  5  1.? 

32.  How  many  feet  in  18  inches?     In  24  in.? 

33.  How  many  yards  m  6  ft.?  In  10  ft.? 
In  11  ft.? 

34.  How  many  leagues  in  6  miles?     In  13  m.  ? 

35.  How  many  inches  in  ^  foot?  In  -^  foot? 
In  li  ft.  ?  In  2i  ft.  ?  In  3i  ft.  ?  In  4i  ft.  ? 
In  5^  ft.  ? 

36.  How  many  feet  in  i  yard  ?  In  1  yd.  ?  In  f 
yd.  ?     In  11  yd.  ?     In  2i  yds.?     In  5f  yds.  ? 

I      37.  How  many  furlongs  in   i  mile?     In  ^  m.  ? 
In   {    m.  ?     In    f    m.?     In    1^    m.  ?      In    2\    m.  ? 
I  lu  3f  m.? 

I      38.  How  many  miles  in  ^  league?     In  i  league? 
I  In  I  league?     In  2\  leagues  ?     In  4i-  leagues  ? 
I      39.  In   2   nails,    how    many  inches?     In  3  na.? 
!  In  4  na.  ? 

I      40.  In  2  yds.,  how  many  quarters  ?     In  3  yds.? 
I  In  4  yds.  ? 

I      41.  In  8   qrs.,  how  many  yards?     In   10  qrs.  ? 
I  In  12  qrs.? 


NUMBERS.  110 

4*2.  In  8  nails,  how  many  quarters?     In  12  na. ? 
Iul7na.? 

43    riow  many  quarters  in  ^  yard  ?     In  2j^  yds.  ? 

44.  How  many  inches  m  i  yd.  ?    In  li  yd.  ?     In 
If  yd.? 

45.  How  many  square  feet  in  ^  square  yard  ?     In 
2i  square  yds.  ?     In  3^  square  yards  ? 

46.  In  2  pints,  how  many  gills  ?     In  3  pts.  ?     In 
6  pts.  ? 

47.  In  3  quarts,  how  many  pints  ?    In  4  qts.  ? 

48.  In  2  gallons,  how  many  quarts  ?     In  5  gals.  ? 
In  6  gals.?     In  7  gals.? 

49.  in  2  barrels,*  how  many  gallons  ? 

50.  In  2  hogsheads,*  how  many  barrels  ? 

51.  In  3   pipes,  how  many    hogsheads?      In  4 
pipes  ?     In  5  pipes  ? 

52.  How  many  pints  in  8  gills  ?     In  13  gills  ?     In 
16  gills?     In  20  gills? 

53.  How  many  quarts  in  4  pts.  ?     In  6  pts.  ?     In 
11  pts.? 

54.  How  many  gallons  in  8  qts.  ?    In  12  qts.  ?    In 
14  qts.  ? 

55.  How  many  gills  in  ^  pint  ?     In  ^  pint  ?     In 
\  pint  ?     In  2i  pints  ?     In  31  pints.? 

,'^6.  How  many  pints  in  \  quart  ?     In  2^^  quarts  ? 
In  3^  quarts  ? 

57.  How  many  quarts  in  ^  gallon  ?     In  ■}■  gal.  ? 
Infgal.  ?    In2igals.  ?    In  31  gals.?    In  5i  gals.? 

58.  How  many  gallons  in  ^  hlid.  ?     In  -^  hhd.  ? 

59.  In  2  pecks,  how  many  quarts  ?     In  4  pks.  ? 
In  6  pecks  ? 

60.  In  2  bushels,  how  many  pecks  ?     In  4  bu.  ? 

*  Wine  measure. 


120  COMPOUND    NXJMBERS. 

61.  In  12  q,uarts,  how  many  pecks?  In  24  qts.  ? 
In  17  qts.  ?     In  28  qts.  ?     In  35  qts.  ? 

62.  In  6  pecks,  how  many  bushels  ?  In  8  pks.  ? 
In  12  pks.? 

63.  How  many  quarts  in  i  peck?  In  ^  pk.  ? 
In  i  pk.  ?     In  2i  pks.  ?     In  3i  pks.  ?     In  5i  pks.  ? 

64.  How  many  quarts  in  ^  bushel  ?  In  -^  bushel  ? 
In  i  bu.  ?     In  i  bu.  ?     In  li  bu.  ?     In  2i  bu.  ? 

65.  How  many  days  in  2  weeks  ?  In  3  weeks  ? 
In  6  weeks  ? 

66.  How  many  hours  in  2  days  ?     In  3  days  ? 

67.  How  many  minutes  in  2  hom's  ?     In  3  hrs.  ? 

68.  How  many  seconds  in  2  min.  ?     In  3  min.  ? 

69.  How  many  seconds  in  ^  minute  ?  In  ^  min.  ? 
In  -fV  inin.  ?     In  -f-  min.  ?     In  1^  min.  ? 

70.  How  many  minutes  in  ^  horn*  ?  In  ^  hour  ? 
In  I  hour  ?    In  ^  hour  ?     In  1  i  hour  ?    In  2i  hours  ? 

71.  How  many  hours  in  -^  day?  In  ^  day  ?  In 
I  day?  In  i  day?  In  f  day  ?  In  f  day  ?  In  i 
day  ?     In  t^  day  ?     In  1^  day  ?     In  2i  days  ? 

72.  How  many  calendar  months  in  -^  year  ?  In  ^ 
year  ?  In  f  year  ?  In  -J-  year  ?  In  f  year  ?  In  i 
year?     In  ^  year?     In  1^  year?     In  3i  years? 

73.  How  many  degrees  in  2  signs  ?    In  3  signs  ? 

74.  How  many  degrees  in  ^  sign?  In  ^  sign? 
[n  ^  sign  ?     In  li  sign  ? 

75.  How  many  units  in  2  dozen  ?  In  3  doz.  ? 
In  4  doz.  ?     In  5  doz.  ?     In  6  doz.  ? 

76.  How  many  units  in  ^  dozea  ?  In  ^  doz.  ?  In  -J 
doa.  ?     In  1  i  doz.  ?     In  2i  doz.  ? 


THE    END. 


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A   COMPLETE   COURSE   OF 


f  mtiml  mli  f  rogrmitre  fet-iffafes, 


THOMSON'S  SERIES  OF  ARITHMETICS. 

This  Series  is  eminently  practical  and  scientific,  giving  the 
"whys"  and  "  wherefores  "  of  every  rule ;  and  containing  much 
raluable  information  not  found  in  other  works  of  the  kind. 

It  is  believed  to  be  the  most  comprehensive,  complete,  and 
carefully  graded  Series  of  Arithmetics  extant. 

TABLE   BOOK.     For  Primary  Schools.      (Revised  and  Enlarged.). 
MENTAL  ARITHMETIC.     For  Beginners,    (ilevised  and  En- 
larged. ) 

RUDIMENTS  OF  ARITHMETIC;  on  Slate and Black- 

BOAHi)  KxEKCiSKS.     (^cwly  Rcviscd  and  Enlarged.) 

ARITHMETICAL    ANALYSIS;  or,  Higher  Mkxtal  Arith- 

MKTIO 

PRACTICAL   ARITHMETIC.      (Revised  and  Enlarged.).  .. 

KEY  TO  PRACTICAL  ARITHMETIC.  (Revised  and  En- 
larged.)  

HIGHERARITHMETIC;  or,THK  Scisnck  and  Application 
OP  Numbers ^- 

KEY  TO  HIGHER  ARITHMETIC 


The   most  liberal  terms  for  first  supplies,  for   introduction, 
and  specimen  copies,  for  examination. 


